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diff --git a/doc/talks/2024-02-03-fosdem/.gitignore b/doc/talks/2024-02-03-fosdem/.gitignore new file mode 100644 index 00000000..9f1f00e6 --- /dev/null +++ b/doc/talks/2024-02-03-fosdem/.gitignore @@ -0,0 +1,17 @@ +* + +!*.txt +!*.md + +!assets + +!.gitignore +!*.svg +!*.png +!*.jpg +!*.tex +!Makefile +!.gitignore +!assets/*.drawio.pdf + +!talk.pdf diff --git a/doc/talks/2024-02-03-fosdem/Makefile b/doc/talks/2024-02-03-fosdem/Makefile new file mode 100644 index 00000000..1440057c --- /dev/null +++ b/doc/talks/2024-02-03-fosdem/Makefile @@ -0,0 +1,30 @@ +ASSETS=assets/consensus.pdf_tex \ + assets/lattice1.pdf_tex \ + assets/lattice2.pdf_tex \ + assets/lattice3.pdf_tex \ + assets/lattice4.pdf_tex \ + assets/lattice5.pdf_tex \ + assets/lattice6.pdf_tex \ + assets/lattice7.pdf_tex \ + assets/lattice8.pdf_tex \ + assets/latticeB_1.pdf_tex \ + assets/latticeB_2.pdf_tex \ + assets/latticeB_3.pdf_tex \ + assets/latticeB_4.pdf_tex \ + assets/latticeB_5.pdf_tex \ + assets/latticeB_6.pdf_tex \ + assets/latticeB_7.pdf_tex \ + assets/latticeB_8.pdf_tex \ + assets/latticeB_9.pdf_tex \ + assets/latticeB_10.pdf_tex \ + ../assets/deuxfleurs.pdf \ + ../assets/timeline-22-24.pdf + +talk.pdf: talk.tex $(ASSETS) + pdflatex talk.tex + +%.pdf: %.svg + inkscape -D -z --file=$^ --export-pdf=$@ + +%.pdf_tex: %.svg + inkscape -D -z --file=$^ --export-pdf=$@ --export-latex diff --git a/doc/talks/2024-02-03-fosdem/abstract.md b/doc/talks/2024-02-03-fosdem/abstract.md new file mode 100644 index 00000000..b2658868 --- /dev/null +++ b/doc/talks/2024-02-03-fosdem/abstract.md @@ -0,0 +1,39 @@ +### (fr) Garage, un système de stockage de données géo-distribué léger et robuste + +Garage est un système de stockage de données léger, géo-distribué, qui +implémente le protocole de stockage S3 de Amazon. Garage est destiné +principalement à l'auto-hébergement sur du matériel courant d'occasion. À ce +titre, il doit tolérer un grand nombre de pannes: coupures de courant, coupures +de connexion Internet, pannes de machines, ... Il doit également être facile à +déployer et à maintenir, afin de pouvoir être facilement utilisé par des +amateurs ou des petites organisations. + +Cette présentation vous proposera un aperçu de Garage et du choix technique +principal qui rend un système comme Garage possible: le refus d'utiliser des +algorithmes de consensus, remplacés avantageusement par des méthodes à +cohérence faible. Notre modèle est fortement inspiré de la base de donnée +Dynamo (DeCandia et al, 2007), et fait usage des types de données CRDT (Shapiro +et al, 2011). Nous exploreront comment ces méthodes s'appliquent à la +construction de l'abstraction "stockage objet" dans un système distribué, et +quelles autres abstractions peuvent ou ne peuvent pas être construites dans ce +modèle. + +### (en) Garage, a lightweight and robust geo-distributed data storage system + +Garage is a lightweight geo-distributed data store that implements the Amazon +S3 object storage protocol. Garage is meant primarily for self-hosting at home +on second-hand commodity hardware, meaning it has to tolerate a wide variety of +failure scenarios such as power cuts, Internet disconnections and machine +crashes. It also has to be easy to deploy and maintain, so that hobbyists and +small organizations can use it without trouble. + +This talk will present Garage and the key technical choice that made Garage +possible: refusing to use consensus algorithms and using instead weak +consistency methods, with a model that is loosely based on that of the Dynamo +database (DeCandia et al, 2007) and that makes heavy use of conflict-free +replicated data types (Shapiro et al, 2011). We will explore how these methods +are suited to building the "object store" abstraction in a distributed system, +and what other abstractions are possible or impossible to build in this model. + + + diff --git a/doc/talks/2024-02-03-fosdem/assets/AGPLv3_Logo.png b/doc/talks/2024-02-03-fosdem/assets/AGPLv3_Logo.png Binary files differnew file mode 100644 index 00000000..445284a3 --- /dev/null +++ b/doc/talks/2024-02-03-fosdem/assets/AGPLv3_Logo.png diff --git a/doc/talks/2024-02-03-fosdem/assets/aerogramme.png b/doc/talks/2024-02-03-fosdem/assets/aerogramme.png Binary files differnew file mode 100644 index 00000000..3aabe3ad --- /dev/null +++ b/doc/talks/2024-02-03-fosdem/assets/aerogramme.png diff --git a/doc/talks/2024-02-03-fosdem/assets/aerogramme.svg b/doc/talks/2024-02-03-fosdem/assets/aerogramme.svg new file mode 100644 index 00000000..0c1ee127 --- /dev/null +++ b/doc/talks/2024-02-03-fosdem/assets/aerogramme.svg @@ -0,0 +1,1241 @@ +<?xml version="1.0" encoding="UTF-8" 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r="2.7302806" /> + <circle + style="fill:#008000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000" + id="path3663-3-0" + cx="18.004833" + cy="30.371933" + r="2.7302806" /> + <circle + style="fill:#800080;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000" + id="path3663-6-6" + cx="18.004833" + cy="21.341394" + r="2.7302806" /> + <text + xml:space="preserve" + style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;stroke-width:0.264583;fill:#000000" + x="6.9525447" + y="13.702217" + id="text3707"><tspan + sodipodi:role="line" + id="tspan3705" + style="stroke-width:0.264583;fill:#000000" + x="6.9525447" + y="13.702217">$write(\{a\})$:</tspan></text> + <text + xml:space="preserve" + style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583" + x="6.9525447" + y="65.261436" + id="text3707-1"><tspan + sodipodi:role="line" + id="tspan3705-5" + style="fill:#000000;stroke-width:0.264583" + x="6.9525447" + y="65.261436">$read()$:</tspan></text> + <text + xml:space="preserve" + style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583" + x="23.457415" + y="24.042637" + id="text3750"><tspan + sodipodi:role="line" + id="tspan3748" + style="fill:#000000;stroke-width:0.264583" + x="23.457415" + y="24.042637">$\sqsupseteq \{a\} \to$ OK</tspan></text> + <text + xml:space="preserve" + style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583" + x="23.457415" + y="33.02087" + id="text3750-3"><tspan + sodipodi:role="line" + id="tspan3748-2" + style="fill:#000000;stroke-width:0.264583" + x="23.457415" + y="33.02087">$\sqsupseteq \{a\} \to$ OK</tspan></text> + <text + xml:space="preserve" + style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583" + x="23.457415" + y="41.972523" + id="text3750-0"><tspan + sodipodi:role="line" + id="tspan3748-6" + style="fill:#999999;stroke-width:0.264583" + x="23.457415" + y="41.972523">$\not\sqsupseteq \{a\}$</tspan></text> + <circle + style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000" + id="path3663-6-6-4" + cx="18.004833" + cy="70.942116" + r="2.7302806" /> + <text + xml:space="preserve" + style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583" + x="23.457415" + y="73.643356" + id="text3750-7"><tspan + sodipodi:role="line" + id="tspan3748-65" + style="fill:#000000;stroke-width:0.264583" + x="23.457415" + y="73.643356">$\to \{\}$</tspan></text> + <text + xml:space="preserve" + style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583" + x="14.395845" + y="52.022549" + id="text4280"><tspan + sodipodi:role="line" + id="tspan4278" + style="fill:#000000;stroke-width:0.264583" + x="14.395845" + y="52.022549">return OK</tspan></text> + </g> +</svg> diff --git 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xml:space="preserve" + style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000" + x="49.27084" + y="40.841526" + id="text1117-3"><tspan + sodipodi:role="line" + id="tspan1115-5" + style="stroke-width:0.264583;fill:#000000" + x="49.27084" + y="40.841526">$\{a,b\}$</tspan></text> + <text + xml:space="preserve" + style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000" + x="176.20593" + y="40.841526" + id="text1117-6"><tspan + sodipodi:role="line" + id="tspan1115-2" + style="stroke-width:0.264583;fill:#000000" + x="176.20593" + y="40.841526">$\{b,c\}$</tspan></text> + </g> + <path + style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2)" + d="M 153.33622,90.367682 118.34198,73.428915" + id="path1300" /> + <path + style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9)" + d="M 177.46016,90.367682 212.4544,73.428915" + id="path1300-2" /> + <path + style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-93)" + d="M 153.33622,61.655656 118.34198,44.716889" + id="path1300-0" /> + <path + style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-7)" + d="M 177.46016,61.655656 212.4544,44.716889" + id="path1300-2-6" /> + <path + style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-93-1)" + d="M 118.34198,61.655656 153.33622,44.716889" + id="path1300-0-7" /> + <path + style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-7-2)" + d="M 212.4544,61.655656 177.46016,44.716889" + id="path1300-2-6-9" /> + <path + style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-93-1-4)" + d="M 118.34198,34.227412 153.33622,17.288645" + id="path1300-0-7-5" /> + <path + style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-7-2-8)" + d="M 212.4544,34.227412 177.46016,17.288645" + id="path1300-2-6-9-0" /> + <path + style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75)" + d="m 228.52843,61.091809 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874" + id="path1300-2-2" + sodipodi:nodetypes="cc" /> + <path + style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75-2)" + d="m 101.90418,61.091809 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874" + id="path1300-2-2-9" + sodipodi:nodetypes="cc" /> + <path + style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75-7)" + d="m 165.29305,89.571762 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874" + id="path1300-2-2-6" + sodipodi:nodetypes="cc" /> + <path + style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75-7-1)" + d="m 165.29305,32.445235 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874" + id="path1300-2-2-6-9" + sodipodi:nodetypes="cc" /> + <circle + style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000" + id="path3663" + cx="147.35568" + cy="95.24971" + r="2.7302806" /> + <circle + style="fill:#008000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000" + id="path3663-3" + cx="126.08154" + cy="67.968384" + r="2.7302806" /> + <circle + style="fill:#800080;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000" + id="path3663-6" + cx="119.58919" + cy="67.645035" + r="2.7302806" /> + <circle + style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000" + id="path3663-1" + cx="18.004833" + cy="39.402473" + r="2.7302806" /> + <circle + style="fill:#008000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000" + id="path3663-3-0" + cx="18.004833" + cy="30.371933" + r="2.7302806" /> + <circle + style="fill:#800080;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000" + id="path3663-6-6" + cx="18.004833" + cy="21.341394" + r="2.7302806" /> + <text + xml:space="preserve" + style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;stroke-width:0.264583;fill:#000000" + x="6.9525447" + y="13.702217" + id="text3707"><tspan + sodipodi:role="line" + id="tspan3705" + style="stroke-width:0.264583;fill:#000000" + x="6.9525447" + y="13.702217">$write(\{a\})$:</tspan></text> + <text + xml:space="preserve" + style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583" + x="6.9525447" + y="65.261436" + id="text3707-1"><tspan + sodipodi:role="line" + id="tspan3705-5" + style="fill:#000000;stroke-width:0.264583" + x="6.9525447" + y="65.261436">$read()$:</tspan></text> + <text + xml:space="preserve" + style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583" + x="23.457415" + y="24.042637" + id="text3750"><tspan + sodipodi:role="line" + id="tspan3748" + style="fill:#000000;stroke-width:0.264583" + x="23.457415" + y="24.042637">$\sqsupseteq \{a\} \to$ OK</tspan></text> + <text + xml:space="preserve" + style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583" + x="23.457415" + y="33.02087" + id="text3750-3"><tspan + sodipodi:role="line" + id="tspan3748-2" + style="fill:#000000;stroke-width:0.264583" + x="23.457415" + y="33.02087">$\sqsupseteq \{a\} \to$ OK</tspan></text> + <text + xml:space="preserve" + style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583" + x="23.457415" + y="41.972523" + id="text3750-0"><tspan + sodipodi:role="line" + id="tspan3748-6" + style="fill:#999999;stroke-width:0.264583" + x="23.457415" + y="41.972523">$\not\sqsupseteq \{a\}$</tspan></text> + <circle + style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000" + id="path3663-6-6-4" + cx="18.004833" + cy="70.942116" + r="2.7302806" /> + <text + xml:space="preserve" + style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583" + x="23.457415" + y="73.643356" + id="text3750-7"><tspan + sodipodi:role="line" + id="tspan3748-65" + style="fill:#000000;stroke-width:0.264583" + x="23.457415" + y="73.643356">$\to \{\}$</tspan></text> + <text + xml:space="preserve" + style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583" + x="14.395845" + y="52.022549" + id="text4280"><tspan + sodipodi:role="line" + id="tspan4278" + style="fill:#000000;stroke-width:0.264583" + x="14.395845" + y="52.022549">return OK</tspan></text> + <text + xml:space="preserve" + style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583" + x="14.395845" + y="92.005798" + id="text4280-3"><tspan + sodipodi:role="line" + id="tspan4278-7" + style="fill:#000000;stroke-width:0.264583" + x="14.395845" + y="92.005798">return $\{\}\sqcup\{a\}=\{a\}$</tspan></text> + <circle + style="fill:#800080;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000" + id="path3663-1-5" + cx="18.004833" + cy="81.007744" + r="2.7302806" /> + <text + xml:space="preserve" + style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583" + x="23.457415" + y="83.577797" + id="text3750-0-6"><tspan + sodipodi:role="line" + id="tspan3748-6-9" + style="fill:#000000;stroke-width:0.264583" + x="23.457415" + y="83.577797">$\to \{a\}$</tspan></text> + </g> +</svg> diff --git a/doc/talks/2024-02-03-fosdem/assets/lattice8.svg b/doc/talks/2024-02-03-fosdem/assets/lattice8.svg new file mode 100644 index 00000000..c94a69b2 --- /dev/null +++ b/doc/talks/2024-02-03-fosdem/assets/lattice8.svg @@ -0,0 +1,581 @@ +<?xml version="1.0" encoding="UTF-8" standalone="no"?> +<!-- Created with Inkscape (http://www.inkscape.org/) --> + +<svg + width="1000" + height="400" + viewBox="0 0 264.58333 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transform="translate(51.996784,1.0317046)" + style="fill:#000000"> + <text + xml:space="preserve" + style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000" + x="112.90984" + y="40.841526" + id="text1117"><tspan + sodipodi:role="line" + id="tspan1115" + style="stroke-width:0.264583;fill:#000000" + x="112.90984" + y="40.841526">$\{a,c\}$</tspan></text> + <text + xml:space="preserve" + style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000" + x="49.27084" + y="40.841526" + id="text1117-3"><tspan + sodipodi:role="line" + id="tspan1115-5" + style="stroke-width:0.264583;fill:#000000" + x="49.27084" + y="40.841526">$\{a,b\}$</tspan></text> + <text + xml:space="preserve" + style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000" + x="176.20593" + y="40.841526" + id="text1117-6"><tspan + sodipodi:role="line" + id="tspan1115-2" + style="stroke-width:0.264583;fill:#000000" + x="176.20593" + y="40.841526">$\{b,c\}$</tspan></text> + </g> + <path + style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2)" + d="M 153.33622,90.367682 118.34198,73.428915" + id="path1300" /> + <path + style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9)" + d="M 177.46016,90.367682 212.4544,73.428915" + id="path1300-2" /> + <path + style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-93)" + d="M 153.33622,61.655656 118.34198,44.716889" + id="path1300-0" /> + <path + style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-7)" + d="M 177.46016,61.655656 212.4544,44.716889" + id="path1300-2-6" /> + <path + style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-93-1)" + d="M 118.34198,61.655656 153.33622,44.716889" + id="path1300-0-7" /> + <path + style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-7-2)" + d="M 212.4544,61.655656 177.46016,44.716889" + id="path1300-2-6-9" /> + <path + style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-93-1-4)" + d="M 118.34198,34.227412 153.33622,17.288645" + id="path1300-0-7-5" /> + <path + style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-7-2-8)" + d="M 212.4544,34.227412 177.46016,17.288645" + id="path1300-2-6-9-0" /> + <path + style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75)" + d="m 228.52843,61.091809 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874" + id="path1300-2-2" + sodipodi:nodetypes="cc" /> + <path + style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75-2)" + d="m 101.90418,61.091809 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874" + id="path1300-2-2-9" + sodipodi:nodetypes="cc" /> + <path + style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75-7)" + d="m 165.29305,89.571762 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874" + id="path1300-2-2-6" + sodipodi:nodetypes="cc" /> + <path + style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75-7-1)" + d="m 165.29305,32.445235 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874" + id="path1300-2-2-6-9" + sodipodi:nodetypes="cc" /> + <circle + style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000" + id="path3663" + cx="132.33408" + cy="68.007973" + r="2.7302806" /> + <circle + style="fill:#008000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000" + id="path3663-3" + cx="126.08154" + cy="67.968384" + r="2.7302806" /> + <circle + style="fill:#800080;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000" + id="path3663-6" + cx="119.58919" + cy="67.645035" + r="2.7302806" /> + <circle + style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000" + id="path3663-1" + cx="18.004833" + cy="39.402473" + r="2.7302806" /> + <circle + style="fill:#008000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000" + id="path3663-3-0" + cx="18.004833" + cy="30.371933" + r="2.7302806" /> + <circle + style="fill:#800080;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000" + id="path3663-6-6" + cx="18.004833" + cy="21.341394" + r="2.7302806" /> + <text + xml:space="preserve" + style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;stroke-width:0.264583;fill:#000000" + x="6.9525447" + y="13.702217" + id="text3707"><tspan + sodipodi:role="line" + id="tspan3705" + style="stroke-width:0.264583;fill:#000000" + x="6.9525447" + y="13.702217">$write(\{a\})$:</tspan></text> + <text + xml:space="preserve" + style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583" + x="6.9525447" + y="65.261436" + id="text3707-1"><tspan + sodipodi:role="line" + id="tspan3705-5" + style="fill:#000000;stroke-width:0.264583" + x="6.9525447" + y="65.261436">$read()$:</tspan></text> + <text + xml:space="preserve" + style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583" + x="23.457415" + y="24.042637" + id="text3750"><tspan + sodipodi:role="line" + id="tspan3748" + style="fill:#000000;stroke-width:0.264583" + x="23.457415" + y="24.042637">$\sqsupseteq \{a\} \to$ OK</tspan></text> + <text + xml:space="preserve" + style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583" + x="23.457415" + y="33.02087" + id="text3750-3"><tspan + sodipodi:role="line" + id="tspan3748-2" + style="fill:#000000;stroke-width:0.264583" + x="23.457415" + y="33.02087">$\sqsupseteq \{a\} \to$ OK</tspan></text> + <text + xml:space="preserve" + style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583" + x="23.457415" + y="41.972523" + id="text3750-0"><tspan + sodipodi:role="line" + id="tspan3748-6" + style="fill:#000000;stroke-width:0.264583" + x="23.457415" + y="41.972523">$\sqsupseteq \{a\}$</tspan></text> + <circle + style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000" + id="path3663-6-6-4" + cx="18.004833" + cy="70.942116" + r="2.7302806" /> + <text + xml:space="preserve" + style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583" + x="23.457415" + y="73.643356" + id="text3750-7"><tspan + sodipodi:role="line" + id="tspan3748-65" + style="fill:#000000;stroke-width:0.264583" + x="23.457415" + y="73.643356">$\to \{\}$</tspan></text> + <text + xml:space="preserve" + style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583" + x="14.395845" + y="52.022549" + id="text4280"><tspan + sodipodi:role="line" + id="tspan4278" + style="fill:#000000;stroke-width:0.264583" + x="14.395845" + y="52.022549">return OK</tspan></text> + <text + xml:space="preserve" + style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583" + x="14.395845" + y="92.005798" + id="text4280-3"><tspan + sodipodi:role="line" + id="tspan4278-7" + style="fill:#000000;stroke-width:0.264583" + x="14.395845" + y="92.005798">return $\{\}\sqcup\{a\}=\{a\}$</tspan></text> + <circle + style="fill:#800080;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000" + id="path3663-1-5" + cx="18.004833" + cy="81.007744" + r="2.7302806" /> + <text + xml:space="preserve" + style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583" + 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style="fill:context-stroke;fill-rule:evenodd;stroke:none" + id="arrow2L-1-9-8" /> + </marker> + <marker + style="overflow:visible" + id="Arrow2-9-75-7" + refX="0" + refY="0" + orient="auto-start-reverse" + inkscape:stockid="Arrow2" + markerWidth="7.6999998" + markerHeight="5.5999999" + viewBox="0 0 7.7 5.6" + inkscape:isstock="true" + inkscape:collect="always" + preserveAspectRatio="xMidYMid"> + <path + transform="scale(0.7)" + d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z" + style="fill:context-stroke;fill-rule:evenodd;stroke:none" + id="arrow2L-1-9-3" /> + </marker> + <marker + style="overflow:visible" + id="Arrow2-9-75-7-1" + refX="0" + refY="0" + orient="auto-start-reverse" + inkscape:stockid="Arrow2" + markerWidth="7.6999998" + markerHeight="5.5999999" + viewBox="0 0 7.7 5.6" + inkscape:isstock="true" + inkscape:collect="always" + preserveAspectRatio="xMidYMid"> + <path + transform="scale(0.7)" + d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z" + style="fill:context-stroke;fill-rule:evenodd;stroke:none" + id="arrow2L-1-9-3-2" /> + </marker> + <marker + style="overflow:visible" + id="Arrow2-93-1-4" + refX="0" + refY="0" + orient="auto-start-reverse" + inkscape:stockid="Arrow2" + markerWidth="7.6999998" + markerHeight="5.5999999" + viewBox="0 0 7.7 5.6" + inkscape:isstock="true" + inkscape:collect="always" + preserveAspectRatio="xMidYMid"> + <path + transform="scale(0.7)" + d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z" + style="fill:context-stroke;fill-rule:evenodd;stroke:none" + id="arrow2L-6-8-7" /> + </marker> + <marker + style="overflow:visible" + id="Arrow2-9-7-2-8" + refX="0" + refY="0" + orient="auto-start-reverse" + inkscape:stockid="Arrow2" + markerWidth="7.6999998" + markerHeight="5.5999999" + viewBox="0 0 7.7 5.6" + inkscape:isstock="true" + inkscape:collect="always" + preserveAspectRatio="xMidYMid"> + <path + transform="scale(0.7)" + d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z" + style="fill:context-stroke;fill-rule:evenodd;stroke:none" + id="arrow2L-1-0-6-4" /> + </marker> + </defs> + <g + inkscape:label="Layer 1" + inkscape:groupmode="layer" + id="layer1" + sodipodi:insensitive="true"> + <rect + style="fill:#ffffff;stroke:none;stroke-width:0.999998;stop-color:#000000" + id="rect288" + width="262.58151" + height="156.82782" + x="0.77790999" + y="0.93738818" /> + </g> + <g + inkscape:groupmode="layer" + id="layer2" + inkscape:label="Layer 2"> + <text + xml:space="preserve" + style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583" + x="164.56372" + y="99.307442" + id="text951"><tspan + sodipodi:role="line" + id="tspan949" + style="fill:#000000;stroke-width:0.264583" + x="164.56372" + y="99.307442">$\{\}$</tspan></text> + <text + xml:space="preserve" + style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583" + x="164.56372" + y="13.151893" + id="text1005"><tspan + sodipodi:role="line" + id="tspan1003" + style="fill:#000000;stroke-width:0.264583" + x="164.56372" + y="13.151893">$\{a,b,c\}$</tspan></text> + <g + id="g1175" + transform="translate(51.996784,3.5774043)"> + <text + xml:space="preserve" + style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583" + x="49.27084" + y="67.008698" + id="text1009"><tspan + sodipodi:role="line" + id="tspan1007" + style="fill:#000000;stroke-width:0.264583" + x="49.27084" + y="67.008698">$\{a\}$</tspan></text> + <text + xml:space="preserve" + style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583" + x="112.90984" + y="67.017166" + id="text1009-3"><tspan + sodipodi:role="line" + id="tspan1007-6" + style="fill:#000000;stroke-width:0.264583" + x="112.90984" + y="67.017166">$\{b\}$</tspan></text> + <text + xml:space="preserve" + style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583" + x="176.20593" + y="67.008698" + id="text1009-7"><tspan + sodipodi:role="line" + id="tspan1007-5" + style="fill:#000000;stroke-width:0.264583" + x="176.20593" + y="67.008698">$\{c\}$</tspan></text> + </g> + <g + id="g1183" + transform="translate(51.996784,1.0317046)" + style="fill:#000000"> + <text + xml:space="preserve" + style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583" + x="112.90984" + y="40.841526" + id="text1117"><tspan + sodipodi:role="line" + id="tspan1115" + style="fill:#000000;stroke-width:0.264583" + x="112.90984" + y="40.841526">$\{a,c\}$</tspan></text> + <text + xml:space="preserve" + style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583" + x="49.27084" + y="40.841526" + id="text1117-3"><tspan + sodipodi:role="line" + id="tspan1115-5" + style="fill:#000000;stroke-width:0.264583" + x="49.27084" + y="40.841526">$\{a,b\}$</tspan></text> + <text + xml:space="preserve" + style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583" + x="176.20593" + y="40.841526" + id="text1117-6"><tspan + sodipodi:role="line" + id="tspan1115-2" + style="fill:#000000;stroke-width:0.264583" + x="176.20593" + y="40.841526">$\{b,c\}$</tspan></text> + </g> + <path + style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2)" + d="M 153.33622,90.367682 118.34198,73.428915" + id="path1300" /> + <path + style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9)" + d="M 177.46016,90.367682 212.4544,73.428915" + id="path1300-2" /> + <path + style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-93)" + d="M 153.33622,61.655656 118.34198,44.716889" + id="path1300-0" /> + <path + style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-7)" + d="M 177.46016,61.655656 212.4544,44.716889" + id="path1300-2-6" /> + <path + style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-93-1)" + d="M 118.34198,61.655656 153.33622,44.716889" + id="path1300-0-7" /> + <path + style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-7-2)" + d="M 212.4544,61.655656 177.46016,44.716889" + id="path1300-2-6-9" /> + <path + style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-93-1-4)" + d="M 118.34198,34.227412 153.33622,17.288645" + id="path1300-0-7-5" /> + <path + style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-7-2-8)" + d="M 212.4544,34.227412 177.46016,17.288645" + id="path1300-2-6-9-0" /> + <path + style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75)" + d="m 228.52843,61.091809 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874" + id="path1300-2-2" + sodipodi:nodetypes="cc" /> + <path + style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75-2)" + d="m 101.90418,61.091809 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874" + id="path1300-2-2-9" + sodipodi:nodetypes="cc" /> + <path + style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75-7)" + d="m 165.29305,89.571762 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874" + id="path1300-2-2-6" + sodipodi:nodetypes="cc" /> + <path + style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75-7-1)" + d="m 165.29305,32.445235 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874" + id="path1300-2-2-6-9" + sodipodi:nodetypes="cc" /> + <circle + style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000" + id="path3663" + cx="147.35568" + cy="95.24971" + r="2.7302806" /> + <circle + style="fill:#008000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000" + id="path3663-3" + cx="176.97627" + cy="68.155472" + r="2.7302806" /> + <circle + style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000" + id="path3663-1" + cx="18.004833" + cy="39.402473" + r="2.7302806" /> + <circle + style="fill:#008000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000" + id="path3663-3-0" + cx="18.004833" + cy="30.371933" + r="2.7302806" /> + <circle + style="fill:#800080;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000" + id="path3663-6-6" + cx="18.004833" + cy="21.341394" + r="2.7302806" /> + <text + xml:space="preserve" + style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583" + x="6.9525447" + y="13.702217" + id="text3707"><tspan + sodipodi:role="line" + id="tspan3705" + style="fill:#000000;stroke-width:0.264583" + x="6.9525447" + y="13.702217">$write(\{a\})$:</tspan></text> + <text + xml:space="preserve" + style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583" + x="23.457415" + y="24.042637" + id="text3750"><tspan + sodipodi:role="line" + id="tspan3748" + style="fill:#000000;stroke-width:0.264583" + x="23.457415" + y="24.042637">$\sqsupseteq \{a\} \to$ OK</tspan></text> + <text + xml:space="preserve" + style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583" + x="23.457415" + y="33.02087" + id="text3750-3"><tspan + sodipodi:role="line" + id="tspan3748-2" + style="fill:#999999;stroke-width:0.264583" + x="23.457415" + y="33.02087">$\not\sqsupseteq \{a\}$</tspan></text> + <text + xml:space="preserve" + style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583" + x="23.457415" + y="41.972523" + id="text3750-0"><tspan + sodipodi:role="line" + id="tspan3748-6" + style="fill:#999999;stroke-width:0.264583" + x="23.457415" + y="41.972523">$\not\sqsupseteq \{a\}$</tspan></text> + <circle + style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000" + id="path3663-1-4" + cx="18.004833" + cy="90.979645" + r="2.7302806" /> + <circle + style="fill:#008000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000" + id="path3663-3-0-5" + cx="18.004833" + cy="81.949104" + r="2.7302806" /> + <circle + style="fill:#800080;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000" + id="path3663-6-6-2" + cx="18.004833" + cy="72.918564" + r="2.7302806" /> + <text + xml:space="preserve" + style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583" + x="6.9525447" + y="65.279381" + id="text3707-5"><tspan + sodipodi:role="line" + id="tspan3705-4" + style="fill:#000000;stroke-width:0.264583" + x="6.9525447" + y="65.279381">$write(\{b\})$:</tspan></text> + <text + xml:space="preserve" + style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583" + x="59.340172" + y="118.94403" + id="text3707-5-3"><tspan + sodipodi:role="line" + id="tspan3705-4-6" + style="fill:#000000;stroke-width:0.264583" + x="59.340172" + y="118.94403">$read()$:</tspan></text> + <text + xml:space="preserve" + style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583" + x="23.457415" + y="75.619804" + id="text3750-7"><tspan + sodipodi:role="line" + id="tspan3748-4" + style="fill:#999999;stroke-width:0.264583" + x="23.457415" + y="75.619804">$\not\sqsupseteq \{b\}$</tspan></text> + <text + xml:space="preserve" + style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583" + x="23.457415" + y="84.598038" + id="text3750-3-4"><tspan + sodipodi:role="line" + id="tspan3748-2-3" + style="fill:#000000;stroke-width:0.264583" + x="23.457415" + y="84.598038">$\sqsupseteq \{b\} \to$ OK</tspan></text> + <text + xml:space="preserve" + style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583" + x="23.457415" + y="93.54969" + id="text3750-0-0"><tspan + sodipodi:role="line" + id="tspan3748-6-7" + style="fill:#999999;stroke-width:0.264583" + x="23.457415" + y="93.54969">$\not\sqsupseteq \{b\}$</tspan></text> + <circle + style="fill:#800080;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000" + id="path3663-6" + cx="118.63729" + cy="67.630196" + r="2.7302806" /> + <circle + style="fill:#800080;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000" + id="path3663-6-6-0" + cx="67.201363" + cy="124.91125" + r="2.7302806" /> + <text + xml:space="preserve" + style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583" + x="72.653946" + y="127.6125" + id="text3750-9"><tspan + sodipodi:role="line" + id="tspan3748-3" + style="fill:#000000;stroke-width:0.264583" + x="72.653946" + y="127.6125">$\to \{a\}$</tspan></text> + <text + xml:space="preserve" + style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583" + x="62.764446" + y="146.3129" + id="text4280-6"><tspan + sodipodi:role="line" + style="fill:#000000;stroke-width:0.264583" + x="62.764446" + y="146.3129" + id="tspan2630">return $\{a\}$</tspan></text> + <circle + style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000" + id="path3663-3-0-7" + cx="67.201363" + cy="133.94179" + r="2.7302806" /> + <text + xml:space="preserve" + style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583" + x="72.653946" + y="136.59073" + id="text3750-3-6"><tspan + sodipodi:role="line" + id="tspan3748-2-0" + style="fill:#000000;stroke-width:0.264583" + x="72.653946" + y="136.59073">$\to \{\}$</tspan></text> + <circle + style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000" + id="path3663-6-6-0-6" + cx="174.36296" + cy="124.91125" + r="2.7302806" /> + <text + xml:space="preserve" + style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583" + x="179.81555" + y="127.6125" + id="text3750-9-1"><tspan + sodipodi:role="line" + id="tspan3748-3-8" + style="fill:#000000;stroke-width:0.264583" + x="179.81555" + y="127.6125">$\to \{\}$</tspan></text> + <text + xml:space="preserve" + style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583" + x="162.7999" + y="118.94403" + id="text3707-5-3-7"><tspan + sodipodi:role="line" + id="tspan3705-4-6-5" + style="fill:#000000;stroke-width:0.264583" + x="162.7999" + y="118.94403">$read()$:</tspan></text> + <text + xml:space="preserve" + style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;stroke-width:0.264583" + x="134.97845" + y="132.58472" + id="text3899"><tspan + sodipodi:role="line" + id="tspan3897" + style="stroke-width:0.264583" + x="134.97845" + y="132.58472">;</tspan></text> + <text + xml:space="preserve" + style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583" + x="169.92604" + y="146.3129" + id="text4280-6-7"><tspan + sodipodi:role="line" + style="fill:#000000;stroke-width:0.264583" + x="169.92604" + y="146.3129" + id="tspan2630-9">return $\{b\}$</tspan></text> + <circle + style="fill:#008000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000" + id="path3663-3-0-7-2" + cx="174.36296" + cy="133.94179" + r="2.7302806" /> + <text + xml:space="preserve" + style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583" + x="179.81555" + y="136.59073" + id="text3750-3-6-0"><tspan + sodipodi:role="line" + id="tspan3748-2-0-2" + style="fill:#000000;stroke-width:0.264583" + x="179.81555" + y="136.59073">$\to \{b\}$</tspan></text> + <text + xml:space="preserve" + style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:end;text-anchor:end;fill:#ff0000;stroke-width:0.264583" + x="259.75" + y="135.53111" + id="text9043"><tspan + sodipodi:role="line" + id="tspan9041" + style="fill:#ff0000;stroke-width:0.264583" + x="259.75" + y="135.53111">${\Large\textbf{??!}}$~~~~~</tspan><tspan + sodipodi:role="line" + style="fill:#ff0000;stroke-width:0.264583" + x="259.75" + y="146.11446" + id="tspan9372">$\{a\} \not\sqsubseteq \{b\}$</tspan></text> + </g> +</svg> diff --git a/doc/talks/2024-02-03-fosdem/assets/latticeB_2.svg b/doc/talks/2024-02-03-fosdem/assets/latticeB_2.svg new file mode 100644 index 00000000..c07cba2b --- /dev/null +++ b/doc/talks/2024-02-03-fosdem/assets/latticeB_2.svg @@ -0,0 +1,576 @@ +<?xml version="1.0" encoding="UTF-8" standalone="no"?> +<!-- Created with Inkscape (http://www.inkscape.org/) --> + +<svg + width="1000" + height="600" + viewBox="0 0 264.58333 158.75" + version="1.1" + id="svg5" + inkscape:version="1.2.2 (b0a8486541, 2022-12-01)" + sodipodi:docname="latticeB_2.svg" + xmlns:inkscape="http://www.inkscape.org/namespaces/inkscape" + xmlns:sodipodi="http://sodipodi.sourceforge.net/DTD/sodipodi-0.dtd" + xmlns="http://www.w3.org/2000/svg" + xmlns:svg="http://www.w3.org/2000/svg"> + <sodipodi:namedview + id="namedview7" + pagecolor="#ffffff" + bordercolor="#666666" + borderopacity="1.0" + inkscape:showpageshadow="2" + 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y="93.54969">$\not\sqsupseteq \{b\}$</tspan></text> + <circle + style="fill:#800080;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000" + id="path3663-6" + cx="118.63729" + cy="67.630196" + r="2.7302806" /> + <circle + style="fill:#800080;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000" + id="path3663-6-6-0" + cx="67.201363" + cy="124.91125" + r="2.7302806" /> + <text + xml:space="preserve" + style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583" + x="72.653946" + y="127.6125" + id="text3750-9"><tspan + sodipodi:role="line" + id="tspan3748-3" + style="fill:#000000;stroke-width:0.264583" + x="72.653946" + y="127.6125">$\to \{a\}$</tspan></text> + <text + xml:space="preserve" + style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583" + x="62.764446" + y="146.3129" + id="text4280-6"><tspan + sodipodi:role="line" + 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style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583" + x="23.457415" + y="24.042637" + id="text3750"><tspan + sodipodi:role="line" + id="tspan3748" + style="fill:#000000;stroke-width:0.264583" + x="23.457415" + y="24.042637">$\sqsupseteq \{a\} \to$ OK</tspan></text> + <text + xml:space="preserve" + style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583" + x="23.457415" + y="33.02087" + id="text3750-3"><tspan + sodipodi:role="line" + id="tspan3748-2" + style="fill:#999999;stroke-width:0.264583" + x="23.457415" + y="33.02087">$\not\sqsupseteq \{a\}$</tspan></text> + <text + xml:space="preserve" + style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583" + x="23.457415" + y="41.972523" + id="text3750-0"><tspan + sodipodi:role="line" + id="tspan3748-6" + style="fill:#999999;stroke-width:0.264583" + x="23.457415" + y="41.972523">$\not\sqsupseteq \{a\}$</tspan></text> + <circle + style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000" + id="path3663-1-4" + cx="18.004833" + cy="90.979645" + r="2.7302806" /> + <circle + style="fill:#008000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000" + id="path3663-3-0-5" + cx="18.004833" + cy="81.949104" + r="2.7302806" /> + <circle + style="fill:#800080;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000" + id="path3663-6-6-2" + cx="18.004833" + cy="72.918564" + r="2.7302806" /> + <text + xml:space="preserve" + style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583" + x="6.9525447" + y="65.279381" + id="text3707-5"><tspan + sodipodi:role="line" + id="tspan3705-4" + style="fill:#000000;stroke-width:0.264583" + x="6.9525447" + y="65.279381">$write(\{b\})$:</tspan></text> + <text + xml:space="preserve" + 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OK</tspan></text> + <text + xml:space="preserve" + style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583" + x="23.457415" + y="93.54969" + id="text3750-0-0"><tspan + sodipodi:role="line" + id="tspan3748-6-7" + style="fill:#999999;stroke-width:0.264583" + x="23.457415" + y="93.54969">$\not\sqsupseteq \{b\}$</tspan></text> + <circle + style="fill:#800080;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000" + id="path3663-6" + cx="118.63729" + cy="67.630196" + r="2.7302806" /> + <circle + style="fill:#800080;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000" + id="path3663-6-6-0" + cx="67.201363" + cy="124.91125" + r="2.7302806" /> + <text + xml:space="preserve" + style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583" + x="72.653946" + y="127.6125" + id="text3750-9"><tspan + sodipodi:role="line" + id="tspan3748-3" + style="fill:#000000;stroke-width:0.264583" + x="72.653946" + y="127.6125">$\to \{a\}$</tspan></text> + <text + xml:space="preserve" + style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583" + x="62.764446" + y="146.3129" + id="text4280-6"><tspan + sodipodi:role="line" + style="fill:#000000;stroke-width:0.264583" + x="62.764446" + y="146.3129" + id="tspan2630">return $\{a\}$</tspan></text> + <circle + style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000" + id="path3663-3-0-7" + cx="67.201363" + cy="133.94179" + r="2.7302806" /> + <text + xml:space="preserve" + style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583" + x="72.653946" + y="136.59073" + id="text3750-3-6"><tspan + sodipodi:role="line" + id="tspan3748-2-0" + style="fill:#000000;stroke-width:0.264583" + x="72.653946" + y="136.59073">$\to \{\}$</tspan></text> + <text + xml:space="preserve" + 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OK</tspan></text> + <text + xml:space="preserve" + style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583" + x="23.457415" + y="93.54969" + id="text3750-0-0"><tspan + sodipodi:role="line" + id="tspan3748-6-7" + style="fill:#999999;stroke-width:0.264583" + x="23.457415" + y="93.54969">$\not\sqsupseteq \{b\}$</tspan></text> + <circle + style="fill:#800080;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000" + id="path3663-6" + cx="118.63729" + cy="67.630196" + r="2.7302806" /> + <circle + style="fill:#800080;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000" + id="path3663-6-6-0" + cx="67.201363" + cy="124.91125" + r="2.7302806" /> + <text + xml:space="preserve" + style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583" + x="72.653946" + y="127.6125" + id="text3750-9"><tspan + sodipodi:role="line" + id="tspan3748-3" + style="fill:#000000;stroke-width:0.264583" + x="72.653946" + y="127.6125">$\to \{a\}$</tspan></text> + <text + xml:space="preserve" + style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583" + x="62.764446" + y="146.3129" + id="text4280-6"><tspan + sodipodi:role="line" + style="fill:#000000;stroke-width:0.264583" + x="62.764446" + y="146.3129" + id="tspan2630">return $\{a\}$</tspan></text> + <circle + style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000" + id="path3663-3-0-7" + cx="67.201363" + cy="133.94179" + r="2.7302806" /> + <text + xml:space="preserve" + style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583" + x="72.653946" + y="136.59073" + id="text3750-3-6"><tspan + sodipodi:role="line" + id="tspan3748-2-0" + style="fill:#000000;stroke-width:0.264583" + x="72.653946" + y="136.59073">$\to \{\}$</tspan></text> + <circle + style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000" + id="path3663-6-6-0-6" + cx="174.36296" + cy="124.91125" + r="2.7302806" /> + <text + xml:space="preserve" + style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583" + x="179.81555" + y="127.6125" + id="text3750-9-1"><tspan + sodipodi:role="line" + id="tspan3748-3-8" + style="fill:#000000;stroke-width:0.264583" + x="179.81555" + y="127.6125">$\to \{\}$</tspan></text> + <text + xml:space="preserve" + style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583" + x="162.7999" + y="118.94403" + id="text3707-5-3-7"><tspan + sodipodi:role="line" + id="tspan3705-4-6-5" + style="fill:#000000;stroke-width:0.264583" + x="162.7999" + y="118.94403">$read()$:</tspan></text> + <text + xml:space="preserve" + style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;stroke-width:0.264583" + x="134.97845" + 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+\usepackage[utf8]{inputenc} +% \usepackage[frenchb]{babel} +\usepackage{amsmath} +\usepackage{mathtools} +\usepackage{breqn} +\usepackage{multirow} +\usetheme{boxes} +\usepackage{graphicx} +\usepackage{import} +\usepackage{adjustbox} +%\useoutertheme[footline=authortitle,subsection=false]{miniframes} +%\useoutertheme[footline=authorinstitute,subsection=false]{miniframes} +\useoutertheme{infolines} +\setbeamertemplate{headline}{} + +\beamertemplatenavigationsymbolsempty + +\definecolor{TitleOrange}{RGB}{255,137,0} +\setbeamercolor{title}{fg=TitleOrange} +\setbeamercolor{frametitle}{fg=TitleOrange} + +\definecolor{ListOrange}{RGB}{255,145,5} +\setbeamertemplate{itemize item}{\color{ListOrange}$\blacktriangleright$} + +\definecolor{verygrey}{RGB}{70,70,70} +\setbeamercolor{normal text}{fg=verygrey} + + +\usepackage{tabu} +\usepackage{multicol} +\usepackage{vwcol} +\usepackage{stmaryrd} +\usepackage{graphicx} + +\usepackage[normalem]{ulem} + +\AtBeginSection[]{ + \begin{frame} + \vfill + \centering + \begin{beamercolorbox}[sep=8pt,center,shadow=true,rounded=true]{title} + \usebeamerfont{title}\insertsectionhead\par% + \end{beamercolorbox} + \vfill + \end{frame} +} + +\title{Garage, the low-tech storage platform for geo-distributed clusters} +\author{Alex Auvolat, Deuxfleurs} +\date{FOSDEM'24, 2024-02-03} + +\begin{document} + +\begin{frame} + \centering + \includegraphics[width=.3\linewidth]{../../sticker/Garage.png} + \vspace{1em} + + {\large\bf Alex Auvolat, Deuxfleurs Association} + \vspace{1em} + + \url{https://garagehq.deuxfleurs.fr/} + + Matrix channel: \texttt{\#garage:deuxfleurs.fr} +\end{frame} + +\begin{frame} + \frametitle{Who I am} + \begin{columns}[t] + \begin{column}{.2\textwidth} + \centering + \adjincludegraphics[width=.4\linewidth, valign=t]{../assets/alex.jpg} + \end{column} + \begin{column}{.6\textwidth} + \textbf{Alex Auvolat}\\ + PhD; co-founder of Deuxfleurs + \end{column} + \begin{column}{.2\textwidth} + ~ + \end{column} + \end{columns} + \vspace{2em} + + \begin{columns}[t] + \begin{column}{.2\textwidth} + \centering + \adjincludegraphics[width=.5\linewidth, valign=t]{../assets/deuxfleurs.pdf} + \end{column} + \begin{column}{.6\textwidth} + \textbf{Deuxfleurs}\\ + A non-profit self-hosting collective,\\ + member of the CHATONS network + \end{column} + \begin{column}{.2\textwidth} + \centering + \adjincludegraphics[width=.7\linewidth, valign=t]{../assets/logo_chatons.png} + \end{column} + \end{columns} + +\end{frame} + +\begin{frame} + \frametitle{Our objective at Deuxfleurs} + + \begin{center} + \textbf{Promote self-hosting and small-scale hosting\\ + as an alternative to large cloud providers} + \end{center} + \vspace{2em} + \visible<2->{ + Why is it hard? + } + \visible<3->{ + \vspace{2em} + \begin{center} + \textbf{\underline{Resilience}}\\ + {\footnotesize (we want good uptime/availability with low supervision)} + \end{center} + } +\end{frame} + +\begin{frame} + \frametitle{How to make a \underline{stable} system} + + Enterprise-grade systems typically employ: + \vspace{1em} + \begin{itemize} + \item RAID + \item Redundant power grid + UPS + \item Redundant Internet connections + \item Low-latency links + \item ... + \end{itemize} + \vspace{1em} + $\to$ it's costly and only worth it at DC scale +\end{frame} + +\begin{frame} + \frametitle{How to make a \underline{resilient} system} + + \only<1,4-5>{ + Instead, we use: + \vspace{1em} + \begin{itemize} + \item \textcolor<2->{gray}{Commodity hardware (e.g. old desktop PCs)} + \vspace{.5em} + \item<4-> \textcolor<5->{gray}{Commodity Internet (e.g. FTTB, FTTH) and power grid} + \vspace{.5em} + \item<5-> \textcolor<6->{gray}{\textbf{Geographical redundancy} (multi-site replication)} + \end{itemize} + } + \only<2>{ + \begin{center} + \includegraphics[width=.8\linewidth]{../assets/neptune.jpg} + \end{center} + } + \only<3>{ + \begin{center} + \includegraphics[width=.8\linewidth]{../assets/atuin.jpg} + \end{center} + } + \only<6>{ + \begin{center} + \includegraphics[width=.8\linewidth]{../assets/inframap_jdll2023.pdf} + \end{center} + } +\end{frame} + +\begin{frame} + \frametitle{Object storage: a crucial component} + \begin{center} + \includegraphics[height=6em]{../assets/Amazon-S3.jpg} + \hspace{3em} + \includegraphics[height=5em]{../assets/minio.png} + \hspace{3em} + \includegraphics[height=6em]{../../logo/garage_hires_crop.png} + \end{center} + \vspace{1em} + S3: a de-facto standard, many compatible applications + + \vspace{1em} + + MinIO is self-hostable but not suited for geo-distributed deployments + + \vspace{1em} + + \textbf{Garage is a self-hosted drop-in replacement for the Amazon S3 object store} +\end{frame} + +\begin{frame} + \frametitle{CRDTs / weak consistency instead of consensus} + Consensus can be implemented reasonably well in practice, so why avoid it? + \vspace{1em} + \begin{itemize} + \item \textbf{Software complexity} + \vspace{1em} + \item \textbf{Performance issues:} + \vspace{.5em} + \begin{itemize} + \item The leader is a \textbf{bottleneck} for all requests\\ + \vspace{.5em} + \item \textbf{Sensitive to higher latency} between nodes + \vspace{.5em} + \item \textbf{Takes time to reconverge} when disrupted (e.g. node going down) + \end{itemize} + \end{itemize} + \vspace{2em} + $\to$ Garage uses only CRDTs internally (conflict-free replicated data types) +\end{frame} + +\begin{frame} + \frametitle{The data model of object storage} + Object storage is basically a key-value store: + \vspace{1em} + + {\footnotesize + \begin{center} + \begin{tabular}{|l|p{8cm}|} + \hline + \textbf{Key: file path + name} & \textbf{Value: file data + metadata} \\ + \hline + \hline + \texttt{index.html} & + \texttt{Content-Type: text/html; charset=utf-8} \newline + \texttt{Content-Length: 24929} \newline + \texttt{<binary blob>} \\ + \hline + \texttt{img/logo.svg} & + \texttt{Content-Type: text/svg+xml} \newline + \texttt{Content-Length: 13429} \newline + \texttt{<binary blob>} \\ + \hline + \texttt{download/index.html} & + \texttt{Content-Type: text/html; charset=utf-8} \newline + \texttt{Content-Length: 26563} \newline + \texttt{<binary blob>} \\ + \hline + \end{tabular} + \end{center} + } + + \vspace{1em} + Simple interface, compatible with many existing applications + + \vspace{1em} + Maps well to CRDT data types +\end{frame} + +\begin{frame} + \frametitle{Performance gains in practice} + \begin{center} + \includegraphics[width=.8\linewidth]{../assets/endpoint_latency_0.7_0.8_minio.png} + \end{center} +\end{frame} + +\begin{frame} + \frametitle{Timeline} + \begin{center} + \includegraphics[width=.8\linewidth]{../assets/timeline-22-24.pdf} + \end{center} +\end{frame} + +% ====================== v0.7.0 =============================== + +\begin{frame} + \frametitle{April 2022 - Garage v0.7.0} + Focus on \underline{observability and ecosystem integration} + \vspace{2em} + \begin{itemize} + \item \textbf{Monitoring:} metrics and traces, using OpenTelemetry + \vspace{1em} + \item Alternative replication modes with 1 or 2 copies,\\ + modes with weaker consistency + \vspace{1em} + \item Kubernetes integration + \vspace{1em} + \item Admin API (v0.7.2) + \vspace{1em} + \item Experimental K2V API (v0.7.2) + \end{itemize} +\end{frame} + +\begin{frame} + \frametitle{Metrics (Prometheus + Grafana)} + \begin{center} + \includegraphics[width=.9\linewidth]{../assets/grafana_dashboard.png} + \end{center} +\end{frame} + +\begin{frame} + \frametitle{Traces (Jaeger)} + \begin{center} + \includegraphics[width=.8\linewidth]{../assets/jaeger_listobjects.png} + \end{center} +\end{frame} + +% ====================== v0.8.0 =============================== + +\begin{frame} + \frametitle{November 2022 - Garage v0.8.0} + Focus on \underline{performance} + \vspace{2em} + \begin{itemize} + \item \textbf{Alternative metadata DB engines} (LMDB, Sqlite) + \vspace{1em} + \item \textbf{Performance improvements:} block streaming, various optimizations... + \vspace{1em} + \item Bucket quotas (max size, max \#objects) + \vspace{1em} + \item Quality of life improvements, observability, etc. + \end{itemize} +\end{frame} + +\begin{frame} + \frametitle{About metadata DB engines} + Issues with Sled: + \vspace{2em} + \begin{itemize} + \item Huge files on disk + \vspace{.5em} + \item Unpredictable performance, especially on HDD + \vspace{.5em} + \item API limitations + \vspace{.5em} + \item Not actively maintained + \end{itemize} + \vspace{2em} + LMDB: very stable, good performance, reasonably small files on disk + + \vspace{1em} + Sled will be removed in Garage v1.0 +\end{frame} + +\begin{frame} + \frametitle{DB engine performance comparison} + \begin{center} + \includegraphics[width=.6\linewidth]{../assets/db_engine.png} + \end{center} + NB: Sqlite was slow due to synchronous journaling mode, now configurable +\end{frame} + +\begin{frame} + \frametitle{Block streaming} + \begin{center} + \only<1>{\includegraphics[width=.8\linewidth]{../assets/schema-streaming-1.png}} + \only<2>{\includegraphics[width=.8\linewidth]{../assets/schema-streaming-2.png}} + \end{center} +\end{frame} + +\begin{frame} + \frametitle{TTFB benchmark} + \begin{center} + \includegraphics[width=.8\linewidth]{../assets/ttfb.png} + \end{center} +\end{frame} + +\begin{frame} + \frametitle{Throughput benchmark} + \begin{center} + \includegraphics[width=.7\linewidth]{../assets/io-0.7-0.8-minio.png} + \end{center} +\end{frame} + +% ====================== v0.9.0 =============================== + +\begin{frame} + \frametitle{October 2023 - Garage v0.9.0} + Focus on \underline{streamlining \& usability} + \vspace{2em} + \begin{itemize} + \item Support multiple HDDs per node + \vspace{1em} + \item S3 compatibility: + \vspace{1em} + \begin{itemize} + \item support basic lifecycle configurations + \vspace{.5em} + \item allow for multipart upload part retries + \end{itemize} + \vspace{1em} + \item LMDB by default, deprecation of Sled + \vspace{1em} + \item New layout computation algorithm + \end{itemize} +\end{frame} + + +\begin{frame} + \frametitle{Layout computation} + \begin{center} + \includegraphics[width=\linewidth]{../assets/location-aware.png} + \end{center} + \vspace{2em} + Garage replicates data on different zones when possible +\end{frame} + +\begin{frame} + \frametitle{Layout computation} + \begin{center} + \includegraphics[width=.8\linewidth]{../assets/map.png} + \end{center} +\end{frame} + +\begin{frame} + \frametitle{Optimal layout computation} + \begin{center} + \includegraphics[width=.6\linewidth]{../assets/geodistrib_paper.png} + \end{center} +\end{frame} + +\begin{frame} + \frametitle{What a "layout" is} + \textbf{A layout is a precomputed index table} + \vspace{2em} + + \begin{center} + \begin{tabular}{|l|l|l|l|} + \hline + \textbf{Partition} & \textbf{Node 1} & \textbf{Node 2} & \textbf{Node 3} \\ + \hline + \hline + Partition 0 & Io (jupiter) & Drosera (atuin) & Courgette (neptune) \\ + \hline + Partition 1 & Datura (atuin) & Courgette (neptune) & Io (jupiter) \\ + \hline + Partition 2 & Io(jupiter) & Celeri (neptune) & Drosera (atuin) \\ + \hline + \hspace{1em}$\vdots$ & \hspace{1em}$\vdots$ & \hspace{1em}$\vdots$ & \hspace{1em}$\vdots$ \\ + \hline + Partition 255 & Concombre (neptune) & Io (jupiter) & Drosera (atuin) \\ + \hline + \end{tabular} + \end{center} + + \vspace{1em} + The index table is built centrally using an optimal algorithm,\\ + then propagated to all nodes +\end{frame} + +\begin{frame} + \frametitle{The relationship between \emph{partition} and \emph{partition key}} + \begin{center} + \begin{tabular}{|l|l|l|l|} + \hline + \textbf{Partition key} & \textbf{Partition} & \textbf{Sort key} & \textbf{Value} \\ + \hline + \hline + \texttt{website} & Partition 12 & \texttt{index.html} & (file data) \\ + \hline + \texttt{website} & Partition 12 & \texttt{img/logo.svg} & (file data) \\ + \hline + \texttt{website} & Partition 12 &\texttt{download/index.html} & (file data) \\ + \hline + \hline + \texttt{backup} & Partition 42 & \texttt{borg/index.2822} & (file data) \\ + \hline + \texttt{backup} & Partition 42 & \texttt{borg/data/2/2329} & (file data) \\ + \hline + \texttt{backup} & Partition 42 & \texttt{borg/data/2/2680} & (file data) \\ + \hline + \hline + \texttt{private} & Partition 42 & \texttt{qq3a2nbe1qjq0ebbvo6ocsp6co} & (file data) \\ + \hline + \end{tabular} + \end{center} + \vspace{1em} + \textbf{To read or write an item:} hash partition key + \\ \hspace{5cm} $\to$ determine partition number (first 8 bits) + \\ \hspace{5cm} $\to$ find associated nodes +\end{frame} + +% ====================== v0.10.0 =============================== + +\begin{frame} + \frametitle{October 2023 - Garage v0.10.0 beta} + Focus on \underline{consistency} + \vspace{2em} + \begin{itemize} + \item Fix consistency issues when reshuffling data + \end{itemize} +\end{frame} + + + + +% -------------------------------------------------------------------- +% ================================================================================= +% ================================================================================= +% -------------------------------------------------------------------- +% -------------------------------------------------------------------- +% -------------------------------------------------------------------- +% ================================================================================= +% ================================================================================= +% -------------------------------------------------------------------- + + + + +\begin{frame} + \frametitle{Two big problems} + \begin{enumerate} + \item \textbf{How to place data on different nodes?}\\ + \vspace{1em} + \underline{Constraints:} heterogeneous hardware\\ + \underline{Objective:} $n$ copies of everything, maximize usable capacity, maximize resilience\\ + \vspace{1em} + $\to$ the Dynamo model + optimization algorithms + \vspace{2em} + \item<2-> \textbf{How to guarantee consistency?}\\ + \vspace{1em} + \underline{Constraints:} slow network (geographical distance), node unavailability/crashes\\ + \underline{Objective:} maximize availability, read-after-write guarantee\\ + \vspace{1em} + $\to$ CRDTs, monotonicity, read and write quorums + \end{enumerate} +\end{frame} + +\section{Problem 1: placing data} + +\begin{frame} + \frametitle{Key-value stores, upgraded: the Dynamo model} + \textbf{Two keys:} + \begin{itemize} + \item Partition key: used to divide data into partitions {\small (a.k.a.~shards)} + \item Sort key: used to identify items inside a partition + \end{itemize} + + \vspace{1em} + + \begin{center} + \begin{tabular}{|l|l|p{3cm}|} + \hline + \textbf{Partition key: bucket} & \textbf{Sort key: filename} & \textbf{Value} \\ + \hline + \hline + \texttt{website} & \texttt{index.html} & (file data) \\ + \hline + \texttt{website} & \texttt{img/logo.svg} & (file data) \\ + \hline + \texttt{website} & \texttt{download/index.html} & (file data) \\ + \hline + \hline + \texttt{backup} & \texttt{borg/index.2822} & (file data) \\ + \hline + \texttt{backup} & \texttt{borg/data/2/2329} & (file data) \\ + \hline + \texttt{backup} & \texttt{borg/data/2/2680} & (file data) \\ + \hline + \hline + \texttt{private} & \texttt{qq3a2nbe1qjq0ebbvo6ocsp6co} & (file data) \\ + \hline + \end{tabular} + \end{center} +\end{frame} + +\begin{frame} + \frametitle{Key-value stores, upgraded: the Dynamo model} + \begin{itemize} + \item Data with different partition keys is stored independently,\\ + on a different set of nodes\\ + \vspace{.5em} + $\to$ no easy way to list all partition keys\\ + $\to$ no cross-shard transactions\\ + \vspace{2em} + \item Placing data: hash the partition key, select nodes accordingly\\ + \vspace{.5em} + $\to$ distributed hash table (DHT) + \vspace{2em} + \item For a given value of the partition key, items can be listed using their sort keys + \end{itemize} +\end{frame} + + +\begin{frame} + \frametitle{Issues with consistent hashing} + \begin{itemize} + \item Consistent hashing doesn't dispatch data based on geographical location of nodes + \vspace{1em} + \item<2-> Geographically aware adaptation, try 1:\\ + data quantities not well balanced between nodes + \vspace{1em} + \item<3-> Geographically aware adaptation, try 2:\\ + too many reshuffles when adding/removing nodes + \end{itemize} +\end{frame} + + +\section{Problem 2: ensuring consistency} + +\begin{frame} + \frametitle{Consensus vs weak consistency} + + \hspace{1em} + \begin{minipage}{7cm} + \textbf{Consensus-based systems:} + \vspace{1em} + \begin{itemize} + \item \textbf{Leader-based:} a leader is elected to coordinate + all reads and writes + \vspace{1em} + \item \textbf{Linearizability} of all operations\\ + (strongest consistency guarantee) + \vspace{1em} + \item Any sequential specification can be implemented as a \textbf{replicated state machine} + \vspace{1em} + \item \textbf{Costly}, the leader is a bottleneck; + leader elections on failure take time + \end{itemize} + \end{minipage} + \hfill + \begin{minipage}{7cm} \visible<2->{ + \textbf{Weakly consistent systems:} + \vspace{1em} + \begin{itemize} + \item \textbf{Nodes are equivalent}, any node + can originate a read or write operation + \vspace{1em} + \item \textbf{Read-after-write consistency} with quorums, + eventual consistency without + \vspace{1em} + \item \textbf{Operations have to commute}, i.e.~we + can only implement CRDTs + \vspace{1em} + \item \textbf{Fast}, no single bottleneck;\\ + works the same with offline nodes + \end{itemize} + } \end{minipage} + \hspace{1em} +\end{frame} + +\begin{frame} + \frametitle{Consensus vs weak consistency} + \begin{center} + \textbf{From a theoretical point of view:}\\ + + \end{center} + \vspace{2em} + + \hspace{1em} + \begin{minipage}{6.5cm} + \underline{Consensus-based systems:} + + \vspace{1em} + + Require \textbf{additional assumptions} such as a fault detector or a strong RNG\\ + (FLP impossibility theorem) + \end{minipage} + \hfill + \begin{minipage}{6.5cm} + \underline{Weakly consistent systems:} + + \vspace{1em} + + Can be implemented in \textbf{any\\asynchronous message passing\\distributed system} with node crashes + \end{minipage} + \hspace{1em} + + \vspace{3em} + \begin{center} + They represent \textbf{different classes of computational capability}\\ + \end{center} +\end{frame} + +\begin{frame} + \frametitle{Consensus vs weak consistency} + \begin{center} + \textbf{The same objects cannot be implemented in both models.} + \end{center} + \vspace{2em} + + \hspace{1em} + \begin{minipage}{6.5cm} + \underline{Consensus-based systems:} + + \vspace{1em} + + \textbf{Any sequential specification}\\~ + + \vspace{1em} + \textbf{Easier to program for}: just write your program as if it were sequential on a single machine + + \end{minipage} + \hfill + \begin{minipage}{6.5cm} + \underline{Weakly consistent systems:} + + \vspace{1em} + + \textbf{Only CRDTs}\\(conflict-free replicated data types) + + \vspace{1em} + Part of the complexity is \textbf{reported to the consumer of the API}\\~ + \end{minipage} + \hspace{1em} +\end{frame} + +\begin{frame} + \frametitle{Understanding the power of consensus} + \textbf{Consensus:} an API with a single operation, $propose(x)$ + \begin{enumerate} + \item nodes all call $propose(x)$ with their proposed value; + \item nodes all receive the same value as a return value, which is one of the proposed values + \end{enumerate} + \vspace{1em} + + \visible<2->{ + \textbf{Equivalent to} a distributed algorithm that gives a total order on all requests + } + \vspace{1em} + + \visible<3->{ + \textbf{Implemented by} this simple replicated state machine: + \vspace{.5em} + \begin{figure} + \centering + \def\svgwidth{.5\textwidth} + \large + \import{assets/}{consensus.pdf_tex} + \end{figure} + \vspace{1em} + } +\end{frame} + +\begin{frame} + \frametitle{Can my object be implemented without consensus?} + \underline{Given the specification of an API:} + \vspace{2em} + \begin{itemize} + \item \textbf{Using this API, we can implement the consensus object} (the $propose$ function)\\ + $\to$ the API is equivalent to consensus/total ordering of messages\\ + $\to$ the API cannot be implemented in a weakly consistent system + \vspace{2em} + \item<2-> \textbf{This API can be implemented using only weak primitives}\\ + (e.g. in the asynchronous message passing model with no further assumption)\\ + $\to$ the API is strictly weaker than consensus\\ + $\to$ we can implement it in Garage! + \end{itemize} +\end{frame} + + +\begin{frame} + \frametitle{What can we implement without consensus?} + \begin{itemize} + \item Any \textbf{conflict-free replicated data type} (CRDT) + \vspace{1em} + \item<2-> Non-transactional key-value stores such as S3 are equivalent to a simple CRDT:\\ + a map of \textbf{last-writer-wins registers} (each key is its own CRDT) + \vspace{1em} + \item<3-> \textbf{Read-after-write consistency} can be implemented + using quorums on read and write operations + \vspace{1em} + \item<4-> \textbf{Monotonicity of reads} can be implemented with repair-on-read\\ + (makes reads more costly, not implemented in Garage) + \end{itemize} +\end{frame} + +\begin{frame} + \frametitle{CRDTs and quorums: read-after-write consistency} + \begin{figure} + \centering + \def\svgwidth{.8\textwidth} + \only<1>{\import{assets/}{lattice1.pdf_tex}}% + \only<2>{\import{assets/}{lattice2.pdf_tex}}% + \only<3>{\import{assets/}{lattice3.pdf_tex}}% + \only<4>{\import{assets/}{lattice4.pdf_tex}}% + \only<5>{\import{assets/}{lattice5.pdf_tex}}% + \only<6>{\import{assets/}{lattice6.pdf_tex}}% + \only<7>{\import{assets/}{lattice7.pdf_tex}}% + \only<8>{\import{assets/}{lattice8.pdf_tex}}% + \end{figure} +\end{frame} + +\begin{frame} + \frametitle{CRDTs and quorums: read-after-write consistency} + \textbf{Property:} If node $A$ did an operation $write(x)$ and received an OK response,\\ + \hspace{2cm} and node $B$ starts an operation $read()$ after $A$ received OK,\\ + \hspace{2cm} then $B$ will read a value $x' \sqsupseteq x$. + + \vspace{1em} + + \hspace{1em} + \begin{minipage}{6.8cm} + \textbf{Algorithm $write(x)$:} + \begin{enumerate} + \item Broadcast $write(x)$ to all nodes + \item Wait for $k > n/2$ nodes to reply OK + \item Return OK + \end{enumerate} + \end{minipage} + \hfill + \begin{minipage}{6.8cm} + \vspace{1em} + \textbf{Algorithm $read()$:} + \begin{enumerate} + \item Broadcast $read()$ to all nodes + \item Wait for $k > n/2$ nodes to reply\\ + with values $x_1, \dots, x_k$ + \item Return $x_1 \sqcup \dots \sqcup x_k$ + \end{enumerate} + \end{minipage} + \hspace{1em} + + \vspace{2em} + \textbf{Why does it work?} There is at least one node at the intersection between the two sets of nodes that replied to each request, that ``saw'' $x$ before the $read()$ started ($x_i \sqsupseteq x$). +\end{frame} + +\begin{frame} + \frametitle{CRDTs and quorums: monotonic-reads consistency} + \begin{figure} + \centering + \def\svgwidth{.8\textwidth} + \only<1>{\import{assets/}{latticeB_1.pdf_tex}}% + \only<2>{\import{assets/}{latticeB_2.pdf_tex}}% + \only<3>{\import{assets/}{latticeB_3.pdf_tex}}% + \only<4>{\import{assets/}{latticeB_4.pdf_tex}}% + \only<5>{\import{assets/}{latticeB_5.pdf_tex}}% + \only<6>{\import{assets/}{latticeB_6.pdf_tex}}% + \only<7>{\import{assets/}{latticeB_7.pdf_tex}}% + \only<8>{\import{assets/}{latticeB_8.pdf_tex}}% + \only<9>{\import{assets/}{latticeB_9.pdf_tex}}% + \only<10>{\import{assets/}{latticeB_10.pdf_tex}}% + \end{figure} +\end{frame} + +\begin{frame} + \frametitle{CRDTs and quorums: monotonic-reads consistency} + \textbf{Property:} If node $A$ did an operation $read()$ and received $x$ as a response,\\ + \hspace{2cm} and node $B$ starts an operation $read()$ after $A$ received $x$,\\ + \hspace{2cm} then $B$ will read a value $x' \sqsupseteq x$. + + \vspace{1em} + + \textbf{Algorithm $monotonic\_read()$:} {\small (a.k.a. repair-on-read)} + \begin{enumerate} + \item Broadcast $read()$ to all nodes + \item Wait for $k > n/2$ nodes to reply with values $x_1, \dots, x_k$ + \item If $x_i \ne x_j$ for some nodes $i$ and $j$,\\ + \hspace{1cm}then call $write(x_1 \sqcup \dots \sqcup x_k)$ and wait for OK from $k' > n/2$ nodes + \item Return $x_1 \sqcup \dots \sqcup x_k$ + \end{enumerate} + + \vspace{1em} + + This makes reads slower in some cases, and is \textbf{not implemented in Garage}. +\end{frame} + +\begin{frame} + \frametitle{A hard problem: layout changes} + \begin{itemize} + \item We rely on quorums $k > n/2$ within each partition:\\ + $$n=3,~~~~~~~k\ge 2$$ + \item<2-> When rebalancing, the set of nodes responsible for a partition can change:\\ + $$\{n_A, n_B, n_C\} \to \{n_A, n_D, n_E\}$$ + \vspace{.01em} + \item<3-> During the rebalancing, $D$ and $E$ don't yet have the data,\\ + ~~~~~~~~~~~~~~~~~~~and $B$ and $C$ want to get rid of the data to free up space\\ + \vspace{.2em} + $\to$ quorums only within the new set of nodes don't work\\ + $\to$ how to coordinate? \textbf{currently, we don't...} + + \end{itemize} +\end{frame} + +\section{Operating big Garage clusters} + +\begin{frame} + \frametitle{Operating Garage} + \begin{center} + \only<1-2>{ + \includegraphics[width=.9\linewidth]{assets/scr_garage_status.png} + \\\vspace{1em} + \visible<2>{\includegraphics[width=.85\linewidth]{assets/scr_garage_status_broken.png}} + } + \end{center} +\end{frame} + +\begin{frame} + \frametitle{Garage's architecture} + \begin{center} + \only<1>{\includegraphics[width=.45\linewidth]{assets/garage.drawio.pdf}}% + \only<2>{\includegraphics[width=.6\linewidth]{assets/garage_sync.drawio.pdf}}% + \end{center} +\end{frame} + +\begin{frame} + \frametitle{Digging deeper} + \begin{center} + \only<1>{\includegraphics[width=.9\linewidth]{assets/scr_garage_stats.png}} + \only<2>{\includegraphics[width=.6\linewidth]{assets/scr_garage_worker_list.png}} + \only<3>{\includegraphics[width=.6\linewidth]{assets/scr_garage_worker_get.png}} + \end{center} +\end{frame} + +\begin{frame} + \frametitle{Potential limitations and bottlenecks} + \begin{itemize} + \item Global: + \begin{itemize} + \item Max. $\sim$100 nodes per cluster (excluding gateways) + \end{itemize} + \vspace{1em} + \item Metadata: + \begin{itemize} + \item One big bucket = bottleneck, object list on 3 nodes only + \end{itemize} + \vspace{1em} + \item Block manager: + \begin{itemize} + \item Lots of small files on disk + \item Processing the resync queue can be slow + \item Multi-HDD support not yet released (soon!) + \end{itemize} + \end{itemize} +\end{frame} + +\begin{frame} + \frametitle{Deployment advice for very large clusters} + \begin{itemize} + \item Metadata storage: + \begin{itemize} + \item ZFS mirror (x2) on fast NVMe + \item Use LMDB storage engine + \end{itemize} + \vspace{.5em} + \item Data block storage: + \begin{itemize} + \item Wait for v0.9 with multi-HDD support + \item XFS on individual drives + \item Increase block size (1MB $\to$ 10MB, requires more RAM and good networking) + \item Tune \texttt{resync-tranquility} and \texttt{resync-worker-count} dynamically + \end{itemize} + \vspace{.5em} + \item Other : + \begin{itemize} + \item Split data over several buckets + \item Use less than 100 storage nodes + \item Use gateway nodes + \end{itemize} + \vspace{.5em} + \end{itemize} + Current deployments: $< 10$ TB, we don't have much experience with more +\end{frame} + +\section{Going further than the S3 API} + +\begin{frame} + \frametitle{Using Garage for everything} + \begin{center} + \only<1>{\includegraphics[width=.8\linewidth]{assets/slideB1.png}}% + \only<2>{\includegraphics[width=.8\linewidth]{assets/slideB2.png}}% + \only<3>{\includegraphics[width=.8\linewidth]{assets/slideB3.png}}% + \end{center} +\end{frame} + +\begin{frame} + \frametitle{K2V Design} + \begin{itemize} + \item A new, custom, minimal API\\ + \vspace{.5em} + \begin{itemize} + \item Single-item operations + \item Operations on ranges and batches of items + \item Polling operations to help implement a PubSub pattern + \end{itemize} + \vspace{1em} + \item<2-> Exposes the partitoning mechanism of Garage\\ + K2V = partition key / sort key / value (like Dynamo) + \vspace{1em} + \item<3-> Weakly consistent, CRDT-friendly\\ + $\to$ no support for transactions (not ACID) + \vspace{1em} + \item<4-> Cryptography-friendly: values are binary blobs + \end{itemize} +\end{frame} + +\begin{frame} + \frametitle{Handling concurrent values} + \textbf{How to handle concurrency?} Example: + \vspace{1em} + \begin{enumerate} + \item Client $A$ reads the initial value of a key, $x_0$ + \vspace{1em} + \item<2-> Client $B$ also reads the initial value $x_0$ of that key + \vspace{1em} + \item<3-> Client $A$ modifies $x_0$, and writes a new value $x_1$ + \vspace{1em} + \item<4-> Client $B$ also modifies $x_0$, and writes a new value $x'_1$,\\ + without having a chance to first read $x_1$\\ + \vspace{1em} + $\to$ what should the final state be? + \end{enumerate} +\end{frame} + +\begin{frame} + \frametitle{Handling concurrent values} + \begin{itemize} + \item If we keep only $x_1$ or $x'_1$, we risk \textbf{loosing application data} + \vspace{1.5em} + \item<2-> Values are opaque binary blobs, \textbf{K2V cannot resolve conflicts} by itself\\ + (e.g. by implementing a CRDT) + \vspace{1.5em} + \item<3-> Solution: \textbf{we keep both!}\\ + $\to$ the value of the key is now $\{x_1, x'_1\}$\\ + $\to$ the client application can decide how to resolve conflicts on the next read + \end{itemize} +\end{frame} + +\begin{frame} + \frametitle{Keeping track of causality} + How does K2V know that $x_1$ and $x'_1$ are concurrent? + \vspace{1em} + \begin{itemize} + \item $read()$ returns \textbf{a set of values} and an associated \textbf{causality token}\\ + \vspace{1.5em} + \item<2-> When calling $write()$, the client sends \textbf{the causality token from its last read} + \vspace{1.5em} + \item<3-> The causality token represents the set of values \textbf{already seen by the client}\\ + $\to$ those values are the \textbf{causal past} of the write operation\\ + $\to$ K2V can keep concurrent values and overwrite all ones in the causal past + \vspace{1.5em} + \item<4-> Internally, the causality token is \textbf{a vector clock} + \end{itemize} +\end{frame} + +\begin{frame} + \frametitle{Application: an e-mail storage server} + \begin{center} + \only<1>{\includegraphics[width=.9\linewidth]{assets/aerogramme.png}}% + \end{center} +\end{frame} + +\begin{frame} + \frametitle{Aerogramme data model} + \begin{center} + \only<1->{\includegraphics[width=.4\linewidth]{assets/aerogramme_datatype.drawio.pdf}}% + \end{center} + \visible<2->{Aerogramme encrypts all stored values for privacy\\ + (Garage server administrators can't read your mail)} +\end{frame} + +\begin{frame} + \frametitle{Different deployment scenarios} + \begin{center} + \only<1>{\includegraphics[width=.9\linewidth]{assets/aerogramme_components1.drawio.pdf}}% + \only<2>{\includegraphics[width=.9\linewidth]{assets/aerogramme_components2.drawio.pdf}}% + \end{center} +\end{frame} + +\begin{frame} + \frametitle{A new model for building resilient software} + How to build an application using only Garage as a data store: + \vspace{1em} + \begin{enumerate} + \item Design a data model suited to K2V\\ + {\footnotesize (see Cassandra docs on porting SQL data models to Cassandra)} + \vspace{1em} + \begin{itemize} + \item Use CRDTs or other eventually consistent data types (see e.g. Bayou) + \vspace{1em} + \item Store opaque binary blobs to provide End-to-End Encryption\\ + \end{itemize} + \vspace{1em} + \item<2-> Store big blobs (files) using the S3 API + \vspace{1em} + \item<3-> Let Garage manage sharding, replication, failover, etc. + \end{enumerate} +\end{frame} + +\section{Conclusion} + +\begin{frame} + \frametitle{Perspectives} + \begin{itemize} + \item Fix the consistency issue when rebalancing + \vspace{1em} + \item Write about Garage's architecture and properties,\\ + and about our proposed architecture for (E2EE) apps over K2V+S3 + \vspace{1em} + \item Continue developing Garage; finish Aerogramme; build new applications... + \vspace{1em} + \item Anything else? + \end{itemize} +\end{frame} + +\begin{frame} + \frametitle{Where to find us} + \begin{center} + \includegraphics[width=.25\linewidth]{../../logo/garage_hires.png}\\ + \vspace{-1em} + \url{https://garagehq.deuxfleurs.fr/}\\ + \url{mailto:garagehq@deuxfleurs.fr}\\ + \texttt{\#garage:deuxfleurs.fr} on Matrix + + \vspace{1.5em} + \includegraphics[width=.06\linewidth]{assets/rust_logo.png} + \includegraphics[width=.13\linewidth]{assets/AGPLv3_Logo.png} + \end{center} +\end{frame} + +\end{document} + +%% vim: set ts=4 sw=4 tw=0 noet spelllang=en : diff --git a/doc/talks/assets/.gitignore b/doc/talks/assets/.gitignore index e483c28f..26848b92 100644 --- a/doc/talks/assets/.gitignore 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