aboutsummaryrefslogtreecommitdiff
path: root/src/rpc/layout/version.rs
blob: 912ee53818dc5688b123cf2d370e18030bc7f3b8 (plain) (blame)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
820
821
822
823
824
825
826
827
828
829
830
831
832
833
834
835
836
837
838
839
840
841
842
843
844
845
846
847
848
use std::collections::HashMap;
use std::collections::HashSet;
use std::convert::TryInto;

use bytesize::ByteSize;
use itertools::Itertools;

use garage_util::crdt::{Crdt, LwwMap};
use garage_util::data::*;
use garage_util::error::*;

use super::graph_algo::*;
use super::schema::*;
use super::*;

// The Message type will be used to collect information on the algorithm.
pub type Message = Vec<String>;

impl LayoutVersion {
	pub fn new(replication_factor: usize) -> Self {
		// We set the default zone redundancy to be Maximum, meaning that the maximum
		// possible value will be used depending on the cluster topology
		let parameters = LayoutParameters {
			zone_redundancy: ZoneRedundancy::Maximum,
		};

		LayoutVersion {
			version: 0,
			replication_factor,
			partition_size: 0,
			roles: LwwMap::new(),
			node_id_vec: Vec::new(),
			nongateway_node_count: 0,
			ring_assignment_data: Vec::new(),
			parameters,
		}
	}

	// ===================== accessors ======================

	/// Returns a list of IDs of nodes that have a role in this
	/// version of the cluster layout, including gateway nodes
	pub fn all_nodes(&self) -> &[Uuid] {
		&self.node_id_vec[..]
	}

	/// Returns a list of IDs of nodes that have a storage capacity
	/// assigned in this version of the cluster layout
	pub fn nongateway_nodes(&self) -> &[Uuid] {
		&self.node_id_vec[..self.nongateway_node_count]
	}

	/// Returns the role of a node in the layout, if it has one
	pub fn node_role(&self, node: &Uuid) -> Option<&NodeRole> {
		match self.roles.get(node) {
			Some(NodeRoleV(Some(v))) => Some(v),
			_ => None,
		}
	}

	/// Returns the capacity of a node in the layout, if it has one
	pub fn get_node_capacity(&self, uuid: &Uuid) -> Option<u64> {
		match self.node_role(uuid) {
			Some(NodeRole {
				capacity: Some(cap),
				zone: _,
				tags: _,
			}) => Some(*cap),
			_ => None,
		}
	}

	/// Returns the number of partitions associated to this node in the ring
	pub fn get_node_usage(&self, uuid: &Uuid) -> Result<usize, Error> {
		for (i, id) in self.node_id_vec.iter().enumerate() {
			if id == uuid {
				let mut count = 0;
				for nod in self.ring_assignment_data.iter() {
					if i as u8 == *nod {
						count += 1
					}
				}
				return Ok(count);
			}
		}
		Err(Error::Message(
			"The Uuid does not correspond to a node present in the \
                    cluster or this node does not have a positive capacity."
				.into(),
		))
	}

	/// Get the partition in which data would fall on
	pub fn partition_of(&self, position: &Hash) -> Partition {
		let top = u16::from_be_bytes(position.as_slice()[0..2].try_into().unwrap());
		top >> (16 - PARTITION_BITS)
	}

	/// Get the list of partitions and the first hash of a partition key that would fall in it
	pub fn partitions(&self) -> impl Iterator<Item = (Partition, Hash)> + '_ {
		(0..(1 << PARTITION_BITS)).map(|i| {
			let top = (i as u16) << (16 - PARTITION_BITS);
			let mut location = [0u8; 32];
			location[..2].copy_from_slice(&u16::to_be_bytes(top)[..]);
			(i as u16, Hash::from(location))
		})
	}

	/// Return the n servers in which data for this hash should be replicated
	pub fn nodes_of(&self, position: &Hash, n: usize) -> impl Iterator<Item = Uuid> + '_ {
		assert_eq!(n, self.replication_factor);

		let data = &self.ring_assignment_data;

		let partition_nodes = if data.len() == self.replication_factor * (1 << PARTITION_BITS) {
			let partition_idx = self.partition_of(position) as usize;
			let partition_start = partition_idx * self.replication_factor;
			let partition_end = (partition_idx + 1) * self.replication_factor;
			&data[partition_start..partition_end]
		} else {
			warn!("Ring not yet ready, read/writes will be lost!");
			&[]
		};

		partition_nodes
			.iter()
			.map(move |i| self.node_id_vec[*i as usize])
	}

	// ===================== internal information extractors ======================

	/// Given a node uuids, this function returns the label of its zone
	pub(crate) fn get_node_zone(&self, uuid: &Uuid) -> Result<&str, Error> {
		match self.node_role(uuid) {
			Some(role) => Ok(&role.zone),
			_ => Err(Error::Message(
				"The Uuid does not correspond to a node present in the cluster.".into(),
			)),
		}
	}

	fn expect_get_node_capacity(&self, uuid: &Uuid) -> u64 {
		self.get_node_capacity(&uuid)
			.expect("non-gateway node with zero capacity")
	}

	/// Returns the sum of capacities of non gateway nodes in the cluster
	fn get_total_capacity(&self) -> Result<u64, Error> {
		let mut total_capacity = 0;
		for uuid in self.nongateway_nodes() {
			total_capacity += self.expect_get_node_capacity(&uuid);
		}
		Ok(total_capacity)
	}

	/// Returns the effective value of the zone_redundancy parameter
	pub(crate) fn effective_zone_redundancy(&self) -> usize {
		match self.parameters.zone_redundancy {
			ZoneRedundancy::AtLeast(v) => v,
			ZoneRedundancy::Maximum => {
				let n_zones = self
					.roles
					.items()
					.iter()
					.filter_map(|(_, _, role)| role.0.as_ref().map(|x| x.zone.as_str()))
					.collect::<HashSet<&str>>()
					.len();
				std::cmp::min(n_zones, self.replication_factor)
			}
		}
	}

	/// Check a cluster layout for internal consistency
	/// (assignment, roles, parameters, partition size)
	/// returns true if consistent, false if error
	pub fn check(&self) -> Result<(), String> {
		// Check that node_id_vec contains the correct list of nodes
		let mut expected_nodes = self
			.roles
			.items()
			.iter()
			.filter(|(_, _, v)| v.0.is_some())
			.map(|(id, _, _)| *id)
			.collect::<Vec<_>>();
		expected_nodes.sort();
		let mut node_id_vec = self.node_id_vec.clone();
		node_id_vec.sort();
		if expected_nodes != node_id_vec {
			return Err(format!("node_id_vec does not contain the correct set of nodes\nnode_id_vec: {:?}\nexpected: {:?}", node_id_vec, expected_nodes));
		}

		// Check that the assignment data has the correct length
		let expected_assignment_data_len = (1 << PARTITION_BITS) * self.replication_factor;
		if self.ring_assignment_data.len() != expected_assignment_data_len {
			return Err(format!(
				"ring_assignment_data has incorrect length {} instead of {}",
				self.ring_assignment_data.len(),
				expected_assignment_data_len
			));
		}

		// Check that the assigned nodes are correct identifiers
		// of nodes that are assigned a role
		// and that role is not the role of a gateway nodes
		for x in self.ring_assignment_data.iter() {
			if *x as usize >= self.node_id_vec.len() {
				return Err(format!(
					"ring_assignment_data contains invalid node id {}",
					*x
				));
			}
			let node = self.node_id_vec[*x as usize];
			match self.roles.get(&node) {
				Some(NodeRoleV(Some(x))) if x.capacity.is_some() => (),
				_ => return Err("ring_assignment_data contains id of a gateway node".into()),
			}
		}

		// Check that every partition is associated to distinct nodes
		let zone_redundancy = self.effective_zone_redundancy();
		let rf = self.replication_factor;
		for p in 0..(1 << PARTITION_BITS) {
			let nodes_of_p = self.ring_assignment_data[rf * p..rf * (p + 1)].to_vec();
			if nodes_of_p.iter().unique().count() != rf {
				return Err(format!("partition does not contain {} unique node ids", rf));
			}
			// Check that every partition is spread over at least zone_redundancy zones.
			let zones_of_p = nodes_of_p
				.iter()
				.map(|n| {
					self.get_node_zone(&self.node_id_vec[*n as usize])
						.expect("Zone not found.")
				})
				.collect::<Vec<_>>();
			if zones_of_p.iter().unique().count() < zone_redundancy {
				return Err(format!(
					"nodes of partition are in less than {} distinct zones",
					zone_redundancy
				));
			}
		}

		// Check that the nodes capacities is consistent with the stored partitions
		let mut node_usage = vec![0; MAX_NODE_NUMBER];
		for n in self.ring_assignment_data.iter() {
			node_usage[*n as usize] += 1;
		}
		for (n, usage) in node_usage.iter().enumerate() {
			if *usage > 0 {
				let uuid = self.node_id_vec[n];
				let partusage = usage * self.partition_size;
				let nodecap = self.expect_get_node_capacity(&uuid);
				if partusage > nodecap {
					return Err(format!(
						"node usage ({}) is bigger than node capacity ({})",
						usage * self.partition_size,
						nodecap
					));
				}
			}
		}

		// Check that the partition size stored is the one computed by the asignation
		// algorithm.
		let cl2 = self.clone();
		let (_, zone_to_id) = cl2.generate_nongateway_zone_ids().unwrap();
		match cl2.compute_optimal_partition_size(&zone_to_id, zone_redundancy) {
			Ok(s) if s != self.partition_size => {
				return Err(format!(
					"partition_size ({}) is different than optimal value ({})",
					self.partition_size, s
				))
			}
			Err(e) => return Err(format!("could not calculate optimal partition size: {}", e)),
			_ => (),
		}

		Ok(())
	}

	// ================== updates to layout, internals ===================

	pub(crate) fn calculate_next_version(
		mut self,
		staging: &LayoutStaging,
	) -> Result<(Self, Message), Error> {
		self.version += 1;

		self.roles.merge(&staging.roles);
		self.roles.retain(|(_, _, v)| v.0.is_some());
		self.parameters = *staging.parameters.get();

		let msg = self.calculate_partition_assignment()?;

		Ok((self, msg))
	}

	/// This function calculates a new partition-to-node assignment.
	/// The computed assignment respects the node replication factor
	/// and the zone redundancy parameter It maximizes the capacity of a
	/// partition (assuming all partitions have the same size).
	/// Among such optimal assignment, it minimizes the distance to
	/// the former assignment (if any) to minimize the amount of
	/// data to be moved.
	/// Staged role changes must be merged with nodes roles before calling this function,
	/// hence it must only be called from apply_staged_changes() and hence is not public.
	fn calculate_partition_assignment(&mut self) -> Result<Message, Error> {
		// We update the node ids, since the node role list might have changed with the
		// changes in the layout. We retrieve the old_assignment reframed with new ids
		let old_assignment_opt = self.update_node_id_vec()?;

		let zone_redundancy = self.effective_zone_redundancy();

		let mut msg = Message::new();
		msg.push("==== COMPUTATION OF A NEW PARTITION ASSIGNATION ====".into());
		msg.push("".into());
		msg.push(format!(
			"Partitions are \
        replicated {} times on at least {} distinct zones.",
			self.replication_factor, zone_redundancy
		));

		// We generate for once numerical ids for the zones of non gateway nodes,
		// to use them as indices in the flow graphs.
		let (id_to_zone, zone_to_id) = self.generate_nongateway_zone_ids()?;

		if self.nongateway_nodes().len() < self.replication_factor {
			return Err(Error::Message(format!(
				"The number of nodes with positive \
            capacity ({}) is smaller than the replication factor ({}).",
				self.nongateway_nodes().len(),
				self.replication_factor
			)));
		}
		if id_to_zone.len() < zone_redundancy {
			return Err(Error::Message(format!(
				"The number of zones with non-gateway \
            nodes ({}) is smaller than the redundancy parameter ({})",
				id_to_zone.len(),
				zone_redundancy
			)));
		}

		// We compute the optimal partition size
		// Capacities should be given in a unit so that partition size is at least 100.
		// In this case, integer rounding plays a marginal role in the percentages of
		// optimality.
		let partition_size = self.compute_optimal_partition_size(&zone_to_id, zone_redundancy)?;

		msg.push("".into());
		if old_assignment_opt.is_some() {
			msg.push(format!(
				"Optimal partition size:                     {} ({} in previous layout)",
				ByteSize::b(partition_size).to_string_as(false),
				ByteSize::b(self.partition_size).to_string_as(false)
			));
		} else {
			msg.push(format!(
				"Optimal partition size:                     {}",
				ByteSize::b(partition_size).to_string_as(false)
			));
		}
		// We write the partition size.
		self.partition_size = partition_size;

		if partition_size < 100 {
			msg.push(
				"WARNING: The partition size is low (< 100), make sure the capacities of your nodes are correct and are of at least a few MB"
					.into(),
			);
		}

		// We compute a first flow/assignment that is heuristically close to the previous
		// assignment
		let mut gflow =
			self.compute_candidate_assignment(&zone_to_id, &old_assignment_opt, zone_redundancy)?;
		if let Some(assoc) = &old_assignment_opt {
			// We minimize the distance to the previous assignment.
			self.minimize_rebalance_load(&mut gflow, &zone_to_id, assoc)?;
		}

		// We display statistics of the computation
		msg.extend(self.output_stat(&gflow, &old_assignment_opt, &zone_to_id, &id_to_zone)?);

		// We update the layout structure
		self.update_ring_from_flow(id_to_zone.len(), &gflow)?;

		if let Err(e) = self.check() {
			return Err(Error::Message(
				format!("Layout check returned an error: {}\nOriginal result of computation: <<<<\n{}\n>>>>", e, msg.join("\n"))
			));
		}

		Ok(msg)
	}

	/// The LwwMap of node roles might have changed. This function updates the node_id_vec
	/// and returns the assignment given by ring, with the new indices of the nodes, and
	/// None if the node is not present anymore.
	/// We work with the assumption that only this function and calculate_new_assignment
	/// do modify assignment_ring and node_id_vec.
	fn update_node_id_vec(&mut self) -> Result<Option<Vec<Vec<usize>>>, Error> {
		// (1) We compute the new node list
		// Non gateway nodes should be coded on 8bits, hence they must be first in the list
		// We build the new node ids
		let new_non_gateway_nodes: Vec<Uuid> = self
			.roles
			.items()
			.iter()
			.filter(|(_, _, v)| matches!(&v.0, Some(r) if r.capacity.is_some()))
			.map(|(k, _, _)| *k)
			.collect();

		if new_non_gateway_nodes.len() > MAX_NODE_NUMBER {
			return Err(Error::Message(format!(
				"There are more than {} non-gateway nodes in the new \
                            layout. This is not allowed.",
				MAX_NODE_NUMBER
			)));
		}

		let new_gateway_nodes: Vec<Uuid> = self
			.roles
			.items()
			.iter()
			.filter(|(_, _, v)| matches!(v, NodeRoleV(Some(r)) if r.capacity.is_none()))
			.map(|(k, _, _)| *k)
			.collect();

		let old_node_id_vec = std::mem::take(&mut self.node_id_vec);

		self.nongateway_node_count = new_non_gateway_nodes.len();
		self.node_id_vec.clear();
		self.node_id_vec.extend(new_non_gateway_nodes);
		self.node_id_vec.extend(new_gateway_nodes);

		let new_node_id_vec = &self.node_id_vec;

		// (2) We retrieve the old association
		// We rewrite the old association with the new indices. We only consider partition
		// to node assignments where the node is still in use.
		if self.ring_assignment_data.is_empty() {
			// This is a new association
			return Ok(None);
		}

		if self.ring_assignment_data.len() != NB_PARTITIONS * self.replication_factor {
			return Err(Error::Message(
				"The old assignment does not have a size corresponding to \
                the old replication factor or the number of partitions."
					.into(),
			));
		}

		// We build a translation table between the uuid and new ids
		let mut uuid_to_new_id = HashMap::<Uuid, usize>::new();

		// We add the indices of only the new non-gateway nodes that can be used in the
		// association ring
		for (i, uuid) in new_node_id_vec.iter().enumerate() {
			uuid_to_new_id.insert(*uuid, i);
		}

		let mut old_assignment = vec![Vec::<usize>::new(); NB_PARTITIONS];
		let rf = self.replication_factor;

		for (p, old_assign_p) in old_assignment.iter_mut().enumerate() {
			for old_id in &self.ring_assignment_data[p * rf..(p + 1) * rf] {
				let uuid = old_node_id_vec[*old_id as usize];
				if uuid_to_new_id.contains_key(&uuid) {
					old_assign_p.push(uuid_to_new_id[&uuid]);
				}
			}
		}

		// We clear the ring assignemnt data
		self.ring_assignment_data = Vec::<CompactNodeType>::new();

		Ok(Some(old_assignment))
	}

	/// This function generates ids for the zone of the nodes appearing in
	/// self.node_id_vec.
	pub(crate) fn generate_nongateway_zone_ids(
		&self,
	) -> Result<(Vec<String>, HashMap<String, usize>), Error> {
		let mut id_to_zone = Vec::<String>::new();
		let mut zone_to_id = HashMap::<String, usize>::new();

		for uuid in self.nongateway_nodes().iter() {
			let r = self.node_role(uuid).unwrap();
			if !zone_to_id.contains_key(&r.zone) && r.capacity.is_some() {
				zone_to_id.insert(r.zone.clone(), id_to_zone.len());
				id_to_zone.push(r.zone.clone());
			}
		}
		Ok((id_to_zone, zone_to_id))
	}

	/// This function computes by dichotomy the largest realizable partition size, given
	/// the layout roles and parameters.
	fn compute_optimal_partition_size(
		&self,
		zone_to_id: &HashMap<String, usize>,
		zone_redundancy: usize,
	) -> Result<u64, Error> {
		let empty_set = HashSet::<(usize, usize)>::new();
		let mut g = self.generate_flow_graph(1, zone_to_id, &empty_set, zone_redundancy)?;
		g.compute_maximal_flow()?;
		if g.get_flow_value()? < (NB_PARTITIONS * self.replication_factor) as i64 {
			return Err(Error::Message(
				"The storage capacity of he cluster is to small. It is \
                       impossible to store partitions of size 1."
					.into(),
			));
		}

		let mut s_down = 1;
		let mut s_up = self.get_total_capacity()?;
		while s_down + 1 < s_up {
			g = self.generate_flow_graph(
				(s_down + s_up) / 2,
				zone_to_id,
				&empty_set,
				zone_redundancy,
			)?;
			g.compute_maximal_flow()?;
			if g.get_flow_value()? < (NB_PARTITIONS * self.replication_factor) as i64 {
				s_up = (s_down + s_up) / 2;
			} else {
				s_down = (s_down + s_up) / 2;
			}
		}

		Ok(s_down)
	}

	fn generate_graph_vertices(nb_zones: usize, nb_nodes: usize) -> Vec<Vertex> {
		let mut vertices = vec![Vertex::Source, Vertex::Sink];
		for p in 0..NB_PARTITIONS {
			vertices.push(Vertex::Pup(p));
			vertices.push(Vertex::Pdown(p));
			for z in 0..nb_zones {
				vertices.push(Vertex::PZ(p, z));
			}
		}
		for n in 0..nb_nodes {
			vertices.push(Vertex::N(n));
		}
		vertices
	}

	/// Generates the graph to compute the maximal flow corresponding to the optimal
	/// partition assignment.
	/// exclude_assoc is the set of (partition, node) association that we are forbidden
	/// to use (hence we do not add the corresponding edge to the graph). This parameter
	/// is used to compute a first flow that uses only edges appearing in the previous
	/// assignment. This produces a solution that heuristically should be close to the
	/// previous one.
	fn generate_flow_graph(
		&self,
		partition_size: u64,
		zone_to_id: &HashMap<String, usize>,
		exclude_assoc: &HashSet<(usize, usize)>,
		zone_redundancy: usize,
	) -> Result<Graph<FlowEdge>, Error> {
		let vertices =
			LayoutVersion::generate_graph_vertices(zone_to_id.len(), self.nongateway_nodes().len());
		let mut g = Graph::<FlowEdge>::new(&vertices);
		let nb_zones = zone_to_id.len();
		for p in 0..NB_PARTITIONS {
			g.add_edge(Vertex::Source, Vertex::Pup(p), zone_redundancy as u64)?;
			g.add_edge(
				Vertex::Source,
				Vertex::Pdown(p),
				(self.replication_factor - zone_redundancy) as u64,
			)?;
			for z in 0..nb_zones {
				g.add_edge(Vertex::Pup(p), Vertex::PZ(p, z), 1)?;
				g.add_edge(
					Vertex::Pdown(p),
					Vertex::PZ(p, z),
					self.replication_factor as u64,
				)?;
			}
		}
		for n in 0..self.nongateway_nodes().len() {
			let node_capacity = self.expect_get_node_capacity(&self.node_id_vec[n]);
			let node_zone = zone_to_id[self.get_node_zone(&self.node_id_vec[n])?];
			g.add_edge(Vertex::N(n), Vertex::Sink, node_capacity / partition_size)?;
			for p in 0..NB_PARTITIONS {
				if !exclude_assoc.contains(&(p, n)) {
					g.add_edge(Vertex::PZ(p, node_zone), Vertex::N(n), 1)?;
				}
			}
		}
		Ok(g)
	}

	/// This function computes a first optimal assignment (in the form of a flow graph).
	fn compute_candidate_assignment(
		&self,
		zone_to_id: &HashMap<String, usize>,
		prev_assign_opt: &Option<Vec<Vec<usize>>>,
		zone_redundancy: usize,
	) -> Result<Graph<FlowEdge>, Error> {
		// We list the (partition,node) associations that are not used in the
		// previous assignment
		let mut exclude_edge = HashSet::<(usize, usize)>::new();
		if let Some(prev_assign) = prev_assign_opt {
			let nb_nodes = self.nongateway_nodes().len();
			for (p, prev_assign_p) in prev_assign.iter().enumerate() {
				for n in 0..nb_nodes {
					exclude_edge.insert((p, n));
				}
				for n in prev_assign_p.iter() {
					exclude_edge.remove(&(p, *n));
				}
			}
		}

		// We compute the best flow using only the edges used in the previous assignment
		let mut g = self.generate_flow_graph(
			self.partition_size,
			zone_to_id,
			&exclude_edge,
			zone_redundancy,
		)?;
		g.compute_maximal_flow()?;

		// We add the excluded edges and compute the maximal flow with the full graph.
		// The algorithm is such that it will start with the flow that we just computed
		// and find ameliorating paths from that.
		for (p, n) in exclude_edge.iter() {
			let node_zone = zone_to_id[self.get_node_zone(&self.node_id_vec[*n])?];
			g.add_edge(Vertex::PZ(*p, node_zone), Vertex::N(*n), 1)?;
		}
		g.compute_maximal_flow()?;
		Ok(g)
	}

	/// This function updates the flow graph gflow to minimize the distance between
	/// its corresponding assignment and the previous one
	fn minimize_rebalance_load(
		&self,
		gflow: &mut Graph<FlowEdge>,
		zone_to_id: &HashMap<String, usize>,
		prev_assign: &[Vec<usize>],
	) -> Result<(), Error> {
		// We define a cost function on the edges (pairs of vertices) corresponding
		// to the distance between the two assignments.
		let mut cost = CostFunction::new();
		for (p, assoc_p) in prev_assign.iter().enumerate() {
			for n in assoc_p.iter() {
				let node_zone = zone_to_id[self.get_node_zone(&self.node_id_vec[*n])?];
				cost.insert((Vertex::PZ(p, node_zone), Vertex::N(*n)), -1);
			}
		}

		// We compute the maximal length of a simple path in gflow. It is used in the
		// Bellman-Ford algorithm in optimize_flow_with_cost to set the number
		// of iterations.
		let nb_nodes = self.nongateway_nodes().len();
		let path_length = 4 * nb_nodes;
		gflow.optimize_flow_with_cost(&cost, path_length)?;

		Ok(())
	}

	/// This function updates the assignment ring from the flow graph.
	fn update_ring_from_flow(
		&mut self,
		nb_zones: usize,
		gflow: &Graph<FlowEdge>,
	) -> Result<(), Error> {
		self.ring_assignment_data = Vec::<CompactNodeType>::new();
		for p in 0..NB_PARTITIONS {
			for z in 0..nb_zones {
				let assoc_vertex = gflow.get_positive_flow_from(Vertex::PZ(p, z))?;
				for vertex in assoc_vertex.iter() {
					if let Vertex::N(n) = vertex {
						self.ring_assignment_data.push((*n).try_into().unwrap());
					}
				}
			}
		}

		if self.ring_assignment_data.len() != NB_PARTITIONS * self.replication_factor {
			return Err(Error::Message(
				"Critical Error : the association ring we produced does not \
                       have the right size."
					.into(),
			));
		}
		Ok(())
	}

	/// This function returns a message summing up the partition repartition of the new
	/// layout, and other statistics of the partition assignment computation.
	fn output_stat(
		&self,
		gflow: &Graph<FlowEdge>,
		prev_assign_opt: &Option<Vec<Vec<usize>>>,
		zone_to_id: &HashMap<String, usize>,
		id_to_zone: &[String],
	) -> Result<Message, Error> {
		let mut msg = Message::new();

		let used_cap = self.partition_size * NB_PARTITIONS as u64 * self.replication_factor as u64;
		let total_cap = self.get_total_capacity()?;
		let percent_cap = 100.0 * (used_cap as f32) / (total_cap as f32);
		msg.push(format!(
			"Usable capacity / total cluster capacity:   {} / {} ({:.1} %)",
			ByteSize::b(used_cap).to_string_as(false),
			ByteSize::b(total_cap).to_string_as(false),
			percent_cap
		));
		msg.push(format!(
			"Effective capacity (replication factor {}):  {}",
			self.replication_factor,
			ByteSize::b(used_cap / self.replication_factor as u64).to_string_as(false)
		));
		if percent_cap < 80. {
			msg.push("".into());
			msg.push(
				"If the percentage is too low, it might be that the \
            cluster topology and redundancy constraints are forcing the use of nodes/zones with small \
            storage capacities."
					.into(),
			);
			msg.push(
				"You might want to move storage capacity between zones or relax the redundancy constraint."
					.into(),
			);
			msg.push(
				"See the detailed statistics below and look for saturated nodes/zones.".into(),
			);
		}

		// We define and fill in the following tables
		let storing_nodes = self.nongateway_nodes();
		let mut new_partitions = vec![0; storing_nodes.len()];
		let mut stored_partitions = vec![0; storing_nodes.len()];

		let mut new_partitions_zone = vec![0; id_to_zone.len()];
		let mut stored_partitions_zone = vec![0; id_to_zone.len()];

		for p in 0..NB_PARTITIONS {
			for z in 0..id_to_zone.len() {
				let pz_nodes = gflow.get_positive_flow_from(Vertex::PZ(p, z))?;
				if !pz_nodes.is_empty() {
					stored_partitions_zone[z] += 1;
					if let Some(prev_assign) = prev_assign_opt {
						let mut old_zones_of_p = Vec::<usize>::new();
						for n in prev_assign[p].iter() {
							old_zones_of_p
								.push(zone_to_id[self.get_node_zone(&self.node_id_vec[*n])?]);
						}
						if !old_zones_of_p.contains(&z) {
							new_partitions_zone[z] += 1;
						}
					}
				}
				for vert in pz_nodes.iter() {
					if let Vertex::N(n) = *vert {
						stored_partitions[n] += 1;
						if let Some(prev_assign) = prev_assign_opt {
							if !prev_assign[p].contains(&n) {
								new_partitions[n] += 1;
							}
						}
					}
				}
			}
		}

		if prev_assign_opt.is_none() {
			new_partitions = stored_partitions.clone();
			//new_partitions_zone = stored_partitions_zone.clone();
		}

		// We display the statistics

		msg.push("".into());
		if prev_assign_opt.is_some() {
			let total_new_partitions: usize = new_partitions.iter().sum();
			msg.push(format!(
				"A total of {} new copies of partitions need to be \
                             transferred.",
				total_new_partitions
			));
			msg.push("".into());
		}

		let mut table = vec![];
		for z in 0..id_to_zone.len() {
			let mut nodes_of_z = Vec::<usize>::new();
			for n in 0..storing_nodes.len() {
				if self.get_node_zone(&self.node_id_vec[n])? == id_to_zone[z] {
					nodes_of_z.push(n);
				}
			}
			let replicated_partitions: usize =
				nodes_of_z.iter().map(|n| stored_partitions[*n]).sum();
			table.push(format!(
				"{}\tTags\tPartitions\tCapacity\tUsable capacity",
				id_to_zone[z]
			));

			let available_cap_z: u64 = self.partition_size * replicated_partitions as u64;
			let mut total_cap_z = 0;
			for n in nodes_of_z.iter() {
				total_cap_z += self.expect_get_node_capacity(&self.node_id_vec[*n]);
			}
			let percent_cap_z = 100.0 * (available_cap_z as f32) / (total_cap_z as f32);

			for n in nodes_of_z.iter() {
				let available_cap_n = stored_partitions[*n] as u64 * self.partition_size;
				let total_cap_n = self.expect_get_node_capacity(&self.node_id_vec[*n]);
				let tags_n = (self.node_role(&self.node_id_vec[*n]).ok_or("<??>"))?.tags_string();
				table.push(format!(
					"  {:?}\t{}\t{} ({} new)\t{}\t{} ({:.1}%)",
					self.node_id_vec[*n],
					tags_n,
					stored_partitions[*n],
					new_partitions[*n],
					ByteSize::b(total_cap_n).to_string_as(false),
					ByteSize::b(available_cap_n).to_string_as(false),
					(available_cap_n as f32) / (total_cap_n as f32) * 100.0,
				));
			}

			table.push(format!(
				"  TOTAL\t\t{} ({} unique)\t{}\t{} ({:.1}%)",
				replicated_partitions,
				stored_partitions_zone[z],
				//new_partitions_zone[z],
				ByteSize::b(total_cap_z).to_string_as(false),
				ByteSize::b(available_cap_z).to_string_as(false),
				percent_cap_z
			));
			table.push("".into());
		}
		msg.push(format_table::format_table_to_string(table));

		Ok(msg)
	}
}