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, 846 insertions, 0 deletions

diff --git a/src/rpc/layout/version.rs b/src/rpc/layout/version.rs
new file mode 100644
index 00000000..ee4b2821
--- /dev/null
+++ b/src/rpc/layout/version.rs
@@ -0,0 +1,846 @@
+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::*;
+
+// 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,
+		}
+	}
+
+	/// Given a node uuids, this function returns the label of its zone if it has one
+	pub fn get_node_zone(&self, uuid: &Uuid) -> Option<&str> {
+		match self.node_role(uuid) {
+			Some(role) => Some(&role.zone),
+			_ => 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 ======================
+
+	pub(crate) fn expect_get_node_capacity(&self, uuid: &Uuid) -> u64 {
+		self.get_node_capacity(uuid)
+			.expect("non-gateway node with zero capacity")
+	}
+
+	pub(crate) fn expect_get_node_zone(&self, uuid: &Uuid) -> &str {
+		self.get_node_zone(uuid).expect("node without a zone")
+	}
+
+	/// Returns the sum of capacities of non gateway nodes in the cluster
+	fn get_total_capacity(&self) -> u64 {
+		let mut total_capacity = 0;
+		for uuid in self.nongateway_nodes() {
+			total_capacity += self.expect_get_node_capacity(uuid);
+		}
+		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 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 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 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.expect_get_node_zone(&self.node_id_vec[*n as usize]))
+				.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.expect_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.expect_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.expect_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.expect_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.expect_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)
+	}
+}