Merge pull request 'NLnet task 3' (#667) from nlnet-task3 into next-0.10

Reviewed-on: https://git.deuxfleurs.fr/Deuxfleurs/garage/pulls/667

1 files changed, 405 insertions, 0 deletions

diff --git a/src/rpc/layout/graph_algo.rs b/src/rpc/layout/graph_algo.rs
new file mode 100644
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+++ b/src/rpc/layout/graph_algo.rs
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+//! This module deals with graph algorithms.
+//! It is used in layout.rs to build the partition to node assignment.
+
+use rand::prelude::{SeedableRng, SliceRandom};
+use std::cmp::{max, min};
+use std::collections::HashMap;
+use std::collections::VecDeque;
+
+/// Vertex data structures used in all the graphs used in layout.rs.
+/// usize parameters correspond to node/zone/partitions ids.
+/// To understand the vertex roles below, please refer to the formal description
+/// of the layout computation algorithm.
+#[derive(Clone, Copy, Debug, PartialEq, Eq, Hash)]
+pub enum Vertex {
+	Source,
+	Pup(usize),       // The vertex p+ of partition p
+	Pdown(usize),     // The vertex p- of partition p
+	PZ(usize, usize), // The vertex corresponding to x_(partition p, zone z)
+	N(usize),         // The vertex corresponding to node n
+	Sink,
+}
+
+/// Edge data structure for the flow algorithm.
+#[derive(Clone, Copy, Debug)]
+pub struct FlowEdge {
+	cap: u64,    // flow maximal capacity of the edge
+	flow: i64,   // flow value on the edge
+	dest: usize, // destination vertex id
+	rev: usize,  // index of the reversed edge (v, self) in the edge list of vertex v
+}
+
+/// Edge data structure for the detection of negative cycles.
+#[derive(Clone, Copy, Debug)]
+pub struct WeightedEdge {
+	w: i64, // weight of the edge
+	dest: usize,
+}
+
+pub trait Edge: Clone + Copy {}
+impl Edge for FlowEdge {}
+impl Edge for WeightedEdge {}
+
+/// Struct for the graph structure. We do encapsulation here to be able to both
+/// provide user friendly Vertex enum to address vertices, and to use internally usize
+/// indices and Vec instead of HashMap in the graph algorithm to optimize execution speed.
+pub struct Graph<E: Edge> {
+	vertex_to_id: HashMap<Vertex, usize>,
+	id_to_vertex: Vec<Vertex>,
+
+	// The graph is stored as an adjacency list
+	graph: Vec<Vec<E>>,
+}
+
+pub type CostFunction = HashMap<(Vertex, Vertex), i64>;
+
+impl<E: Edge> Graph<E> {
+	pub fn new(vertices: &[Vertex]) -> Self {
+		let mut map = HashMap::<Vertex, usize>::new();
+		for (i, vert) in vertices.iter().enumerate() {
+			map.insert(*vert, i);
+		}
+		Graph::<E> {
+			vertex_to_id: map,
+			id_to_vertex: vertices.to_vec(),
+			graph: vec![Vec::<E>::new(); vertices.len()],
+		}
+	}
+
+	fn get_vertex_id(&self, v: &Vertex) -> Result<usize, String> {
+		self.vertex_to_id
+			.get(v)
+			.cloned()
+			.ok_or_else(|| format!("The graph does not contain vertex {:?}", v))
+	}
+}
+
+impl Graph<FlowEdge> {
+	/// This function adds a directed edge to the graph with capacity c, and the
+	/// corresponding reversed edge with capacity 0.
+	pub fn add_edge(&mut self, u: Vertex, v: Vertex, c: u64) -> Result<(), String> {
+		let idu = self.get_vertex_id(&u)?;
+		let idv = self.get_vertex_id(&v)?;
+		if idu == idv {
+			return Err("Cannot add edge from vertex to itself in flow graph".into());
+		}
+
+		let rev_u = self.graph[idu].len();
+		let rev_v = self.graph[idv].len();
+		self.graph[idu].push(FlowEdge {
+			cap: c,
+			dest: idv,
+			flow: 0,
+			rev: rev_v,
+		});
+		self.graph[idv].push(FlowEdge {
+			cap: 0,
+			dest: idu,
+			flow: 0,
+			rev: rev_u,
+		});
+		Ok(())
+	}
+
+	/// This function returns the list of vertices that receive a positive flow from
+	/// vertex v.
+	pub fn get_positive_flow_from(&self, v: Vertex) -> Result<Vec<Vertex>, String> {
+		let idv = self.get_vertex_id(&v)?;
+		let mut result = Vec::<Vertex>::new();
+		for edge in self.graph[idv].iter() {
+			if edge.flow > 0 {
+				result.push(self.id_to_vertex[edge.dest]);
+			}
+		}
+		Ok(result)
+	}
+
+	/// This function returns the value of the flow outgoing from v.
+	pub fn get_outflow(&self, v: Vertex) -> Result<i64, String> {
+		let idv = self.get_vertex_id(&v)?;
+		let mut result = 0;
+		for edge in self.graph[idv].iter() {
+			result += max(0, edge.flow);
+		}
+		Ok(result)
+	}
+
+	/// This function computes the flow total value by computing the outgoing flow
+	/// from the source.
+	pub fn get_flow_value(&mut self) -> Result<i64, String> {
+		self.get_outflow(Vertex::Source)
+	}
+
+	/// This function shuffles the order of the edge lists. It keeps the ids of the
+	/// reversed edges consistent.
+	fn shuffle_edges(&mut self) {
+		// We use deterministic randomness so that the layout calculation algorihtm
+		// will output the same thing every time it is run. This way, the results
+		// pre-calculated in `garage layout show` will match exactly those used
+		// in practice with `garage layout apply`
+		let mut rng = rand::rngs::StdRng::from_seed([0x12u8; 32]);
+		for i in 0..self.graph.len() {
+			self.graph[i].shuffle(&mut rng);
+			// We need to update the ids of the reverse edges.
+			for j in 0..self.graph[i].len() {
+				let target_v = self.graph[i][j].dest;
+				let target_rev = self.graph[i][j].rev;
+				self.graph[target_v][target_rev].rev = j;
+			}
+		}
+	}
+
+	/// Computes an upper bound of the flow on the graph
+	pub fn flow_upper_bound(&self) -> Result<u64, String> {
+		let idsource = self.get_vertex_id(&Vertex::Source)?;
+		let mut flow_upper_bound = 0;
+		for edge in self.graph[idsource].iter() {
+			flow_upper_bound += edge.cap;
+		}
+		Ok(flow_upper_bound)
+	}
+
+	/// This function computes the maximal flow using Dinic's algorithm. It starts with
+	/// the flow values already present in the graph. So it is possible to add some edge to
+	/// the graph, compute a flow, add other edges, update the flow.
+	pub fn compute_maximal_flow(&mut self) -> Result<(), String> {
+		let idsource = self.get_vertex_id(&Vertex::Source)?;
+		let idsink = self.get_vertex_id(&Vertex::Sink)?;
+
+		let nb_vertices = self.graph.len();
+
+		let flow_upper_bound = self.flow_upper_bound()?;
+
+		// To ensure the dispersion of the associations generated by the
+		// assignment, we shuffle the neighbours of the nodes. Hence,
+		// the vertices do not consider their neighbours in the same order.
+		self.shuffle_edges();
+
+		// We run Dinic's max flow algorithm
+		loop {
+			// We build the level array from Dinic's algorithm.
+			let mut level = vec![None; nb_vertices];
+
+			let mut fifo = VecDeque::new();
+			fifo.push_back((idsource, 0));
+			while let Some((id, lvl)) = fifo.pop_front() {
+				if level[id].is_none() {
+					// it means id has not yet been reached
+					level[id] = Some(lvl);
+					for edge in self.graph[id].iter() {
+						if edge.cap as i64 - edge.flow > 0 {
+							fifo.push_back((edge.dest, lvl + 1));
+						}
+					}
+				}
+			}
+			if level[idsink].is_none() {
+				// There is no residual flow
+				break;
+			}
+			// Now we run DFS respecting the level array
+			let mut next_nbd = vec![0; nb_vertices];
+			let mut lifo = Vec::new();
+
+			lifo.push((idsource, flow_upper_bound));
+
+			while let Some((id, f)) = lifo.last().cloned() {
+				if id == idsink {
+					// The DFS reached the sink, we can add a
+					// residual flow.
+					lifo.pop();
+					while let Some((id, _)) = lifo.pop() {
+						let nbd = next_nbd[id];
+						self.graph[id][nbd].flow += f as i64;
+						let id_rev = self.graph[id][nbd].dest;
+						let nbd_rev = self.graph[id][nbd].rev;
+						self.graph[id_rev][nbd_rev].flow -= f as i64;
+					}
+					lifo.push((idsource, flow_upper_bound));
+					continue;
+				}
+				// else we did not reach the sink
+				let nbd = next_nbd[id];
+				if nbd >= self.graph[id].len() {
+					// There is nothing to explore from id anymore
+					lifo.pop();
+					if let Some((parent, _)) = lifo.last() {
+						next_nbd[*parent] += 1;
+					}
+					continue;
+				}
+				// else we can try to send flow from id to its nbd
+				let new_flow = min(
+					f as i64,
+					self.graph[id][nbd].cap as i64 - self.graph[id][nbd].flow,
+				) as u64;
+				if new_flow == 0 {
+					next_nbd[id] += 1;
+					continue;
+				}
+				if let (Some(lvldest), Some(lvlid)) = (level[self.graph[id][nbd].dest], level[id]) {
+					if lvldest <= lvlid {
+						// We cannot send flow to nbd.
+						next_nbd[id] += 1;
+						continue;
+					}
+				}
+				// otherwise, we send flow to nbd.
+				lifo.push((self.graph[id][nbd].dest, new_flow));
+			}
+		}
+		Ok(())
+	}
+
+	/// This function takes a flow, and a cost function on the edges, and tries to find an
+	/// equivalent flow with a better cost, by finding improving overflow cycles. It uses
+	/// as subroutine the Bellman Ford algorithm run up to path_length.
+	/// We assume that the cost of edge (u,v) is the opposite of the cost of (v,u), and
+	/// only one needs to be present in the cost function.
+	pub fn optimize_flow_with_cost(
+		&mut self,
+		cost: &CostFunction,
+		path_length: usize,
+	) -> Result<(), String> {
+		// We build the weighted graph g where we will look for negative cycle
+		let mut gf = self.build_cost_graph(cost)?;
+		let mut cycles = gf.list_negative_cycles(path_length);
+		while !cycles.is_empty() {
+			// we enumerate negative cycles
+			for c in cycles.iter() {
+				for i in 0..c.len() {
+					// We add one flow unit to the edge (u,v) of cycle c
+					let idu = self.vertex_to_id[&c[i]];
+					let idv = self.vertex_to_id[&c[(i + 1) % c.len()]];
+					for j in 0..self.graph[idu].len() {
+						// since idu appears at most once in the cycles, we enumerate every
+						// edge at most once.
+						let edge = self.graph[idu][j];
+						if edge.dest == idv {
+							self.graph[idu][j].flow += 1;
+							self.graph[idv][edge.rev].flow -= 1;
+							break;
+						}
+					}
+				}
+			}
+
+			gf = self.build_cost_graph(cost)?;
+			cycles = gf.list_negative_cycles(path_length);
+		}
+		Ok(())
+	}
+
+	/// Construct the weighted graph G_f from the flow and the cost function
+	fn build_cost_graph(&self, cost: &CostFunction) -> Result<Graph<WeightedEdge>, String> {
+		let mut g = Graph::<WeightedEdge>::new(&self.id_to_vertex);
+		let nb_vertices = self.id_to_vertex.len();
+		for i in 0..nb_vertices {
+			for edge in self.graph[i].iter() {
+				if edge.cap as i64 - edge.flow > 0 {
+					// It is possible to send overflow through this edge
+					let u = self.id_to_vertex[i];
+					let v = self.id_to_vertex[edge.dest];
+					if cost.contains_key(&(u, v)) {
+						g.add_edge(u, v, cost[&(u, v)])?;
+					} else if cost.contains_key(&(v, u)) {
+						g.add_edge(u, v, -cost[&(v, u)])?;
+					} else {
+						g.add_edge(u, v, 0)?;
+					}
+				}
+			}
+		}
+		Ok(g)
+	}
+}
+
+impl Graph<WeightedEdge> {
+	/// This function adds a single directed weighted edge to the graph.
+	pub fn add_edge(&mut self, u: Vertex, v: Vertex, w: i64) -> Result<(), String> {
+		let idu = self.get_vertex_id(&u)?;
+		let idv = self.get_vertex_id(&v)?;
+		self.graph[idu].push(WeightedEdge { w, dest: idv });
+		Ok(())
+	}
+
+	/// This function lists the negative cycles it manages to find after path_length
+	/// iterations of the main loop of the Bellman-Ford algorithm. For the classical
+	/// algorithm, path_length needs to be equal to the number of vertices. However,
+	/// for particular graph structures like in our case, the algorithm is still correct
+	/// when path_length is the length of the longest possible simple path.
+	/// See the formal description of the algorithm for more details.
+	fn list_negative_cycles(&self, path_length: usize) -> Vec<Vec<Vertex>> {
+		let nb_vertices = self.graph.len();
+
+		// We start with every vertex at distance 0 of some imaginary extra -1 vertex.
+		let mut distance = vec![0; nb_vertices];
+		// The prev vector collects for every vertex from where does the shortest path come
+		let mut prev = vec![None; nb_vertices];
+
+		for _ in 0..path_length + 1 {
+			for id in 0..nb_vertices {
+				for e in self.graph[id].iter() {
+					if distance[id] + e.w < distance[e.dest] {
+						distance[e.dest] = distance[id] + e.w;
+						prev[e.dest] = Some(id);
+					}
+				}
+			}
+		}
+
+		// If self.graph contains a negative cycle, then at this point the graph described
+		// by prev (which is a directed 1-forest/functional graph)
+		// must contain a cycle. We list the cycles of prev.
+		let cycles_prev = cycles_of_1_forest(&prev);
+
+		// Remark that the cycle in prev is in the reverse order compared to the cycle
+		// in the graph. Thus the .rev().
+		return cycles_prev
+			.iter()
+			.map(|cycle| {
+				cycle
+					.iter()
+					.rev()
+					.map(|id| self.id_to_vertex[*id])
+					.collect()
+			})
+			.collect();
+	}
+}
+
+/// This function returns the list of cycles of a directed 1 forest. It does not
+/// check for the consistency of the input.
+fn cycles_of_1_forest(forest: &[Option<usize>]) -> Vec<Vec<usize>> {
+	let mut cycles = Vec::<Vec<usize>>::new();
+	let mut time_of_discovery = vec![None; forest.len()];
+
+	for t in 0..forest.len() {
+		let mut id = t;
+		// while we are on a valid undiscovered node
+		while time_of_discovery[id].is_none() {
+			time_of_discovery[id] = Some(t);
+			if let Some(i) = forest[id] {
+				id = i;
+			} else {
+				break;
+			}
+		}
+		if forest[id].is_some() && time_of_discovery[id] == Some(t) {
+			// We discovered an id that we explored at this iteration t.
+			// It means we are on a cycle
+			let mut cy = vec![id; 1];
+			let mut id2 = id;
+			while let Some(id_next) = forest[id2] {
+				id2 = id_next;
+				if id2 != id {
+					cy.push(id2);
+				} else {
+					break;
+				}
+			}
+			cycles.push(cy);
+		}
+	}
+	cycles
+}