New version of the algorithm that calculate the layout.

It takes as paramters the replication factor and the zone redundancy, computes the
largest partition size reachable with these constraints, and among the possible
assignation with this partition size, it computes the one that moves the least number
of partitions compared to the previous assignation.
This computation uses graph algorithms defined in graph_algo.rs

1 files changed, 471 insertions, 324 deletions

diff --git a/src/rpc/layout.rs b/src/rpc/layout.rs
index 40f97368..ff60ce98 100644
--- a/src/rpc/layout.rs
+++ b/src/rpc/layout.rs
@@ -1,17 +1,23 @@
-use std::cmp::min;
 use std::cmp::Ordering;
 use std::collections::HashMap;
+use std::collections::HashSet;
+
+use hex::ToHex;
 
 use serde::{Deserialize, Serialize};
 
-use garage_util::bipartite::*;
 use garage_util::crdt::{AutoCrdt, Crdt, LwwMap};
 use garage_util::data::*;
 
-use rand::prelude::SliceRandom;
+use crate::graph_algo::*;
 
 use crate::ring::*;
 
+use std::convert::TryInto;
+
+//The Message type will be used to collect information on the algorithm.
+type Message = Vec<String>;
+
 /// The layout of the cluster, i.e. the list of roles
 /// which are assigned to each cluster node
 #[derive(Clone, Debug, Serialize, Deserialize)]
@@ -19,12 +25,21 @@ pub struct ClusterLayout {
 	pub version: u64,
 
 	pub replication_factor: usize,
+    #[serde(default="default_one")]
+    pub zone_redundancy: usize,
+  
+    //This attribute is only used to retain the previously computed partition size, 
+    //to know to what extent does it change with the layout update.
+    #[serde(default="default_zero")]
+    pub partition_size: u32,
+
 	pub roles: LwwMap<Uuid, NodeRoleV>,
 
 	/// node_id_vec: a vector of node IDs with a role assigned
 	/// in the system (this includes gateway nodes).
 	/// The order here is different than the vec stored by `roles`, because:
-	/// 1. non-gateway nodes are first so that they have lower numbers
+	/// 1. non-gateway nodes are first so that they have lower numbers holding
+    ///     in u8 (the number of non-gateway nodes is at most 256).
 	/// 2. nodes that don't have a role are excluded (but they need to
 	///    stay in the CRDT as tombstones)
 	pub node_id_vec: Vec<Uuid>,
@@ -38,6 +53,15 @@ pub struct ClusterLayout {
 	pub staging_hash: Hash,
 }
 
+fn default_one() -> usize{
+    return 1;
+}
+fn default_zero() -> u32{
+    return 0;
+}
+
+const NB_PARTITIONS : usize = 1usize << PARTITION_BITS;
+
 #[derive(PartialEq, Eq, PartialOrd, Ord, Clone, Debug, Serialize, Deserialize)]
 pub struct NodeRoleV(pub Option<NodeRole>);
 
@@ -66,16 +90,31 @@ impl NodeRole {
 			None => "gateway".to_string(),
 		}
 	}
+
+    pub fn tags_string(&self) -> String {
+        let mut tags = String::new();
+        if self.tags.len() == 0 {
+            return tags
+        }
+        tags.push_str(&self.tags[0].clone());
+        for t in 1..self.tags.len(){
+            tags.push_str(",");
+            tags.push_str(&self.tags[t].clone());
+        }
+        return tags;
+    }
 }
 
 impl ClusterLayout {
-	pub fn new(replication_factor: usize) -> Self {
+	pub fn new(replication_factor: usize, zone_redundancy: usize) -> Self {
 		let empty_lwwmap = LwwMap::new();
 		let empty_lwwmap_hash = blake2sum(&rmp_to_vec_all_named(&empty_lwwmap).unwrap()[..]);
 
 		ClusterLayout {
 			version: 0,
 			replication_factor,
+            zone_redundancy,
+            partition_size: 0,
 			roles: LwwMap::new(),
 			node_id_vec: Vec::new(),
 			ring_assignation_data: Vec::new(),
@@ -122,6 +161,44 @@ impl ClusterLayout {
 		}
 	}
 
+    ///Returns the uuids of the non_gateway nodes in self.node_id_vec.
+    pub fn useful_nodes(&self) -> Vec<Uuid> {
+        let mut result = Vec::<Uuid>::new();
+        for uuid in self.node_id_vec.iter() {
+            match self.node_role(uuid) {
+                Some(role) if role.capacity != None => result.push(*uuid),
+                _ => ()
+            }
+        }
+        return result;
+    }
+
+    ///Given a node uuids, this function returns the label of its zone
+    pub fn get_node_zone(&self, uuid : &Uuid) -> Result<String,String> {
+        match self.node_role(uuid) {
+            Some(role) => return Ok(role.zone.clone()),
+            _ => return Err("The Uuid does not correspond to a node present in the cluster.".to_string())
+        }
+    }
+    
+    ///Given a node uuids, this function returns its capacity or fails if it does not have any
+    pub fn get_node_capacity(&self, uuid : &Uuid) -> Result<u32,String> {
+        match self.node_role(uuid) {
+            Some(NodeRole{capacity : Some(cap), zone: _, tags: _}) => return Ok(*cap),
+            _ => return Err("The Uuid does not correspond to a node present in the cluster or this node does not have a positive capacity.".to_string())
+        }
+    }
+
+    ///Returns the sum of capacities of non gateway nodes in the cluster
+    pub fn get_total_capacity(&self) -> Result<u32,String> {
+        let mut total_capacity = 0;
+        for uuid in self.useful_nodes().iter() {
+            total_capacity += self.get_node_capacity(uuid)?;
+        }
+        return Ok(total_capacity);
+    }
+
+
 	/// Check a cluster layout for internal consistency
 	/// returns true if consistent, false if error
 	pub fn check(&self) -> bool {
@@ -168,342 +245,412 @@ impl ClusterLayout {
 		true
 	}
 
+}
+
+impl ClusterLayout {
 	/// This function calculates a new partition-to-node assignation.
-	/// The computed assignation maximizes the capacity of a
+	/// The computed assignation 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 assignation, it minimizes the distance to
 	/// the former assignation (if any) to minimize the amount of
-	/// data to be moved. A heuristic ensures node triplets
-	/// dispersion (in garage_util::bipartite::optimize_matching()).
-	pub fn calculate_partition_assignation(&mut self) -> bool {
+	/// data to be moved. 
+	pub fn calculate_partition_assignation(&mut self, replication:usize, redundancy:usize) -> Result<Message,String> {
 		//The nodes might have been updated, some might have been deleted.
 		//So we need to first update the list of nodes and retrieve the
 		//assignation.
-		let old_node_assignation = self.update_nodes_and_ring();
-
-		let (node_zone, _) = self.get_node_zone_capacity();
-
-		//We compute the optimal number of partition to assign to
-		//every node and zone.
-		if let Some((part_per_nod, part_per_zone)) = self.optimal_proportions() {
-			//We collect part_per_zone in a vec to not rely on the
-			//arbitrary order in which elements are iterated in
-			//Hashmap::iter()
-			let part_per_zone_vec = part_per_zone
-				.iter()
-				.map(|(x, y)| (x.clone(), *y))
-				.collect::<Vec<(String, usize)>>();
-			//We create an indexing of the zones
-			let mut zone_id = HashMap::<String, usize>::new();
-			for (i, ppz) in part_per_zone_vec.iter().enumerate() {
-				zone_id.insert(ppz.0.clone(), i);
-			}
-
-			//We compute a candidate for the new partition to zone
-			//assignation.
-			let nb_zones = part_per_zone.len();
-			let nb_nodes = part_per_nod.len();
-			let nb_partitions = 1 << PARTITION_BITS;
-			let left_cap_vec = vec![self.replication_factor as u32; nb_partitions];
-			let right_cap_vec = part_per_zone_vec.iter().map(|(_, y)| *y as u32).collect();
-			let mut zone_assignation = dinic_compute_matching(left_cap_vec, right_cap_vec);
-
-			//We create the structure for the partition-to-node assignation.
-			let mut node_assignation = vec![vec![None; self.replication_factor]; nb_partitions];
-			//We will decrement part_per_nod to keep track of the number
-			//of partitions that we still have to associate.
-			let mut part_per_nod = part_per_nod;
-
-			//We minimize the distance to the former assignation(if any)
-
-			//We get the id of the zones of the former assignation
-			//(and the id no_zone if there is no node assignated)
-			let no_zone = part_per_zone_vec.len();
-			let old_zone_assignation: Vec<Vec<usize>> = old_node_assignation
-				.iter()
-				.map(|x| {
-					x.iter()
-						.map(|id| match *id {
-							Some(i) => zone_id[&node_zone[i]],
-							None => no_zone,
-						})
-						.collect()
-				})
-				.collect();
-
-			//We minimize the distance to the former zone assignation
-			zone_assignation =
-				optimize_matching(&old_zone_assignation, &zone_assignation, nb_zones + 1); //+1 for no_zone
-
-			//We need to assign partitions to nodes in their zone
-			//We first put the nodes assignation that can stay the same
-			for i in 0..nb_partitions {
-				for j in 0..self.replication_factor {
-					if let Some(Some(former_node)) = old_node_assignation[i].iter().find(|x| {
-						if let Some(id) = x {
-							zone_id[&node_zone[*id]] == zone_assignation[i][j]
-						} else {
-							false
-						}
-					}) {
-						if part_per_nod[*former_node] > 0 {
-							node_assignation[i][j] = Some(*former_node);
-							part_per_nod[*former_node] -= 1;
-						}
-					}
-				}
-			}
-
-			//We complete the assignation of partitions to nodes
-			let mut rng = rand::thread_rng();
-			for i in 0..nb_partitions {
-				for j in 0..self.replication_factor {
-					if node_assignation[i][j] == None {
-						let possible_nodes: Vec<usize> = (0..nb_nodes)
-							.filter(|id| {
-								zone_id[&node_zone[*id]] == zone_assignation[i][j]
-									&& part_per_nod[*id] > 0
-							})
-							.collect();
-						assert!(!possible_nodes.is_empty());
-						//We randomly pick a node
-						if let Some(nod) = possible_nodes.choose(&mut rng) {
-							node_assignation[i][j] = Some(*nod);
-							part_per_nod[*nod] -= 1;
-						}
-					}
-				}
-			}
-
-			//We write the assignation in the 1D table
-			self.ring_assignation_data = Vec::<CompactNodeType>::new();
-			for ass in node_assignation {
-				for nod in ass {
-					if let Some(id) = nod {
-						self.ring_assignation_data.push(id as CompactNodeType);
-					} else {
-						panic!()
-					}
-				}
-			}
-
-			true
-		} else {
-			false
-		}
-	}
+        
+        //We update the node ids, since the node list might have changed with the staged
+        //changes in the layout. We retrieve the old_assignation reframed with the new ids
+        let old_assignation_opt = self.update_node_id_vec()?;
+        self.replication_factor = replication;
+        self.zone_redundancy = redundancy;
+        
+        let mut msg = Message::new();
+        msg.push(format!("Computation of a new cluster layout where partitions are 
+        replicated {} times on at least {} distinct zones.", replication, redundancy));
+
+        //We generate for once numerical ids for the zone, to use them as indices in the 
+        //flow graphs.
+        let (id_to_zone , zone_to_id) = self.generate_zone_ids()?;
+
+        msg.push(format!("The cluster contains {} nodes spread over {} zones.", 
+                         self.useful_nodes().len(), id_to_zone.len()));
+        
+        //We compute the optimal partition size
+        let partition_size = self.compute_optimal_partition_size(&zone_to_id)?;
+        if old_assignation_opt != None  {
+            msg.push(format!("Given the replication and redundancy constraint, the 
+                optimal size of a partition is {}. In the previous layout, it used to 
+                be {}.", partition_size, self.partition_size));
+        }
+        else {
+            msg.push(format!("Given the replication and redundancy constraints, the 
+                optimal size of a partition is {}.", partition_size));
+        }
+        self.partition_size = partition_size;
+
+        //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_assignation_opt)?;
+
+        if let Some(assoc) = &old_assignation_opt {
+            //We minimize the distance to the previous assignment.
+            self.minimize_rebalance_load(&mut gflow, &zone_to_id, &assoc)?;
+        }
+
+        msg.append(&mut self.output_stat(&gflow, &old_assignation_opt, &zone_to_id,&id_to_zone)?);
+
+        //We update the layout structure
+        self.update_ring_from_flow(id_to_zone.len() , &gflow)?;
+        return Ok(msg);
+    }
 
 	/// The LwwMap of node roles might have changed. This function updates the node_id_vec
 	/// and returns the assignation given by ring, with the new indices of the nodes, and
-	/// None of the node is not present anymore.
+	/// None if the node is not present anymore.
 	/// We work with the assumption that only this function and calculate_new_assignation
 	/// do modify assignation_ring and node_id_vec.
-	fn update_nodes_and_ring(&mut self) -> Vec<Vec<Option<usize>>> {
-		let nb_partitions = 1usize << PARTITION_BITS;
-		let mut node_assignation = vec![vec![None; self.replication_factor]; nb_partitions];
-		let rf = self.replication_factor;
-		let ring = &self.ring_assignation_data;
-
-		let new_node_id_vec: Vec<Uuid> = self.roles.items().iter().map(|(k, _, _)| *k).collect();
-
-		if ring.len() == rf * nb_partitions {
-			for i in 0..nb_partitions {
-				for j in 0..self.replication_factor {
-					node_assignation[i][j] = new_node_id_vec
-						.iter()
-						.position(|id| *id == self.node_id_vec[ring[i * rf + j] as usize]);
-				}
-			}
-		}
-
-		self.node_id_vec = new_node_id_vec;
-		self.ring_assignation_data = vec![];
-		node_assignation
+    fn update_node_id_vec(&mut self) -> Result< Option< Vec<Vec<usize> > > ,String> {
+        // (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 mut new_non_gateway_nodes: Vec<Uuid> = self.roles.items().iter()
+            .filter(|(_, _, v)| 
+                        match &v.0 {Some(r) if r.capacity != None => true, _=> false })
+            .map(|(k, _, _)| *k).collect();
+        
+        if new_non_gateway_nodes.len() > MAX_NODE_NUMBER {
+            return Err(format!("There are more than {} non-gateway nodes in the new layout. This is not allowed.", MAX_NODE_NUMBER).to_string());
+        }
+
+		let mut new_gateway_nodes: Vec<Uuid> = self.roles.items().iter()
+            .filter(|(_, _, v)| 
+                        match v {NodeRoleV(Some(r)) if r.capacity == None => true, _=> false })
+            .map(|(k, _, _)| *k).collect();
+
+        let nb_useful_nodes = new_non_gateway_nodes.len();
+        let mut new_node_id_vec = Vec::<Uuid>::new();
+        new_node_id_vec.append(&mut new_non_gateway_nodes);
+        new_node_id_vec.append(&mut new_gateway_nodes);
+        
+        
+        // (2) We retrieve the old association
+        //We rewrite the old association with the new indices. We only consider partition
+        //to node assignations where the node is still in use.
+        let nb_partitions = 1usize << PARTITION_BITS;
+        let mut old_assignation = vec![ Vec::<usize>::new() ; nb_partitions];
+        
+        if self.ring_assignation_data.len() == 0 {
+            //This is a new association
+            return Ok(None);
+        }
+        if self.ring_assignation_data.len() != nb_partitions * self.replication_factor {
+            return Err("The old assignation does not have a size corresponding to the old replication factor or the number of partitions.".to_string());
+        }
+
+        //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 in 0..nb_useful_nodes {
+            uuid_to_new_id.insert(new_node_id_vec[i], i );
+        }
+
+        let rf= self.replication_factor;
+        for p in 0..nb_partitions {
+            for old_id in &self.ring_assignation_data[p*rf..(p+1)*rf] {
+                let uuid = self.node_id_vec[*old_id as usize];
+                if uuid_to_new_id.contains_key(&uuid) {
+                    old_assignation[p].push(uuid_to_new_id[&uuid]);
+                }
+            }
+        }
+
+        //We write the results
+        self.node_id_vec = new_node_id_vec;
+        self.ring_assignation_data = Vec::<CompactNodeType>::new();
+
+        return Ok(Some(old_assignation));
 	}
 
-	///This function compute the number of partition to assign to
-	///every node and zone, so that every partition is replicated
-	///self.replication_factor times and the capacity of a partition
-	///is maximized.
-	fn optimal_proportions(&mut self) -> Option<(Vec<usize>, HashMap<String, usize>)> {
-		let mut zone_capacity: HashMap<String, u32> = HashMap::new();
-
-		let (node_zone, node_capacity) = self.get_node_zone_capacity();
-		let nb_nodes = self.node_id_vec.len();
-
-		for i in 0..nb_nodes {
-			if zone_capacity.contains_key(&node_zone[i]) {
-				zone_capacity.insert(
-					node_zone[i].clone(),
-					zone_capacity[&node_zone[i]] + node_capacity[i],
-				);
-			} else {
-				zone_capacity.insert(node_zone[i].clone(), node_capacity[i]);
-			}
-		}
-
-		//Compute the optimal number of partitions per zone
-		let sum_capacities: u32 = zone_capacity.values().sum();
-
-		if sum_capacities == 0 {
-			println!("No storage capacity in the network.");
-			return None;
-		}
-
-		let nb_partitions = 1 << PARTITION_BITS;
 
-		//Initially we would like to use zones porportionally to
-		//their capacity.
-		//However, a large zone can be associated to at most
-		//nb_partitions to ensure replication of the date.
-		//So we take the min with nb_partitions:
-		let mut part_per_zone: HashMap<String, usize> = zone_capacity
-			.iter()
-			.map(|(k, v)| {
-				(
-					k.clone(),
-					min(
-						nb_partitions,
-						(self.replication_factor * nb_partitions * *v as usize)
-							/ sum_capacities as usize,
-					),
-				)
-			})
-			.collect();
-
-		//The replication_factor-1 upper bounds the number of
-		//part_per_zones that are greater than nb_partitions
-		for _ in 1..self.replication_factor {
-			//The number of partitions that are not assignated to
-			//a zone that takes nb_partitions.
-			let sum_capleft: u32 = zone_capacity
-				.keys()
-				.filter(|k| part_per_zone[*k] < nb_partitions)
-				.map(|k| zone_capacity[k])
-				.sum();
-
-			//The number of replication of the data that we need
-			//to ensure.
-			let repl_left = self.replication_factor
-				- part_per_zone
-					.values()
-					.filter(|x| **x == nb_partitions)
-					.count();
-			if repl_left == 0 {
-				break;
-			}
-
-			for k in zone_capacity.keys() {
-				if part_per_zone[k] != nb_partitions {
-					part_per_zone.insert(
-						k.to_string(),
-						min(
-							nb_partitions,
-							(nb_partitions * zone_capacity[k] as usize * repl_left)
-								/ sum_capleft as usize,
-						),
-					);
-				}
-			}
-		}
-
-		//Now we divide the zone's partition share proportionally
-		//between their nodes.
-
-		let mut part_per_nod: Vec<usize> = (0..nb_nodes)
-			.map(|i| {
-				(part_per_zone[&node_zone[i]] * node_capacity[i] as usize)
-					/ zone_capacity[&node_zone[i]] as usize
-			})
-			.collect();
-
-		//We must update the part_per_zone to make it correspond to
-		//part_per_nod (because of integer rounding)
-		part_per_zone = part_per_zone.iter().map(|(k, _)| (k.clone(), 0)).collect();
-		for i in 0..nb_nodes {
-			part_per_zone.insert(
-				node_zone[i].clone(),
-				part_per_zone[&node_zone[i]] + part_per_nod[i],
-			);
-		}
-
-		//Because of integer rounding, the total sum of part_per_nod
-		//might not be replication_factor*nb_partitions.
-		// We need at most to add 1 to every non maximal value of
-		// part_per_nod. The capacity of a partition will be bounded
-		// by the minimal value of
-		// node_capacity_vec[i]/part_per_nod[i]
-		// so we try to maximize this minimal value, keeping the
-		// part_per_zone capped
-
-		let discrepancy: usize =
-			nb_partitions * self.replication_factor - part_per_nod.iter().sum::<usize>();
-
-		//We use a stupid O(N^2) algorithm. If the number of nodes
-		//is actually expected to be high, one should optimize this.
-
-		for _ in 0..discrepancy {
-			if let Some(idmax) = (0..nb_nodes)
-				.filter(|i| part_per_zone[&node_zone[*i]] < nb_partitions)
-				.max_by(|i, j| {
-					(node_capacity[*i] * (part_per_nod[*j] + 1) as u32)
-						.cmp(&(node_capacity[*j] * (part_per_nod[*i] + 1) as u32))
-				}) {
-				part_per_nod[idmax] += 1;
-				part_per_zone.insert(
-					node_zone[idmax].clone(),
-					part_per_zone[&node_zone[idmax]] + 1,
-				);
-			}
-		}
-
-		//We check the algorithm consistency
-
-		let discrepancy: usize =
-			nb_partitions * self.replication_factor - part_per_nod.iter().sum::<usize>();
-		assert!(discrepancy == 0);
-		assert!(if let Some(v) = part_per_zone.values().max() {
-			*v <= nb_partitions
-		} else {
-			false
-		});
-
-		Some((part_per_nod, part_per_zone))
-	}
-
-	//Returns vectors of zone and capacity; indexed by the same (temporary)
-	//indices as node_id_vec.
-	fn get_node_zone_capacity(&self) -> (Vec<String>, Vec<u32>) {
-		let node_zone = self
-			.node_id_vec
-			.iter()
-			.map(|id_nod| match self.node_role(id_nod) {
-				Some(NodeRole {
-					zone,
-					capacity: _,
-					tags: _,
-				}) => zone.clone(),
-				_ => "".to_string(),
-			})
-			.collect();
-
-		let node_capacity = self
-			.node_id_vec
-			.iter()
-			.map(|id_nod| match self.node_role(id_nod) {
-				Some(NodeRole {
-					zone: _,
-					capacity: Some(c),
-					tags: _,
-				}) => *c,
-				_ => 0,
-			})
-			.collect();
-
-		(node_zone, node_capacity)
-	}
+    ///This function generates ids for the zone of the nodes appearing in 
+    ///self.node_id_vec.
+    fn generate_zone_ids(&self) -> Result<(Vec<String>, HashMap<String, usize>),String>{
+        let mut id_to_zone = Vec::<String>::new();
+        let mut zone_to_id = HashMap::<String,usize>::new();
+
+        for uuid in self.node_id_vec.iter() {
+            if self.roles.get(uuid) == None {
+                return Err("The uuid was not found in the node roles (this should not happen, it might be a critical error).".to_string());
+            }
+            match self.node_role(&uuid) {
+                Some(r) => if !zone_to_id.contains_key(&r.zone) && r.capacity != None {
+                            zone_to_id.insert(r.zone.clone() , id_to_zone.len());
+                            id_to_zone.push(r.zone.clone());
+                        }
+                _ => ()
+            }
+        }
+        return Ok((id_to_zone, zone_to_id));
+    }
+
+    ///This function computes by dichotomy the largest realizable partition size, given
+    ///the layout.
+    fn compute_optimal_partition_size(&self, zone_to_id: &HashMap<String, usize>) -> Result<u32,String>{
+        let nb_partitions = 1usize << PARTITION_BITS;
+        let empty_set = HashSet::<(usize,usize)>::new();
+        let mut g = self.generate_flow_graph(1, zone_to_id, &empty_set)?;
+        g.compute_maximal_flow()?;
+        if g.get_flow_value()? < (nb_partitions*self.replication_factor).try_into().unwrap() {
+            return Err("The storage capacity of he cluster is to small. It is impossible to store partitions of size 1.".to_string());
+        }
+
+        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)?;
+            g.compute_maximal_flow()?;
+            if g.get_flow_value()? < (nb_partitions*self.replication_factor).try_into().unwrap() {
+                s_up = (s_down+s_up)/2;
+            }
+            else {
+                s_down = (s_down+s_up)/2;
+            }
+        }
+
+        return 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));
+        }
+        return vertices;
+    }
+
+    fn generate_flow_graph(&self, size: u32, zone_to_id: &HashMap<String, usize>, exclude_assoc : &HashSet<(usize,usize)>) -> Result<Graph<FlowEdge>, String> {
+        let vertices = ClusterLayout::generate_graph_vertices(zone_to_id.len(), 
+                                                        self.useful_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), self.zone_redundancy as u32)?;
+            g.add_edge(Vertex::Source, Vertex::Pdown(p), (self.replication_factor - self.zone_redundancy) as u32)?;
+            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 u32)?;
+            }
+        }
+        for n in 0..self.useful_nodes().len() {
+            let node_capacity = self.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/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)?;
+                }
+            }
+        }
+        return Ok(g);
+    }
+
+
+    fn compute_candidate_assignment(&self, zone_to_id: &HashMap<String, usize>, 
+        old_assoc_opt : &Option<Vec< Vec<usize> >>) -> Result<Graph<FlowEdge>, String > {
+        
+        //We list the edges that are not used in the old association
+        let mut exclude_edge = HashSet::<(usize,usize)>::new();
+        if let Some(old_assoc) = old_assoc_opt {
+            let nb_nodes = self.useful_nodes().len();
+            for p in 0..NB_PARTITIONS {
+                for n in 0..nb_nodes {
+                    exclude_edge.insert((p,n));
+                }
+                for n in old_assoc[p].iter() {
+                    exclude_edge.remove(&(p,*n));
+                }
+            }
+        }
+
+        //We compute the best flow using only the edges used in the old assoc
+        let mut g = self.generate_flow_graph(self.partition_size, zone_to_id, &exclude_edge )?;
+        g.compute_maximal_flow()?;
+        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()?;
+        return Ok(g);
+    }
+
+    fn minimize_rebalance_load(&self, gflow: &mut Graph<FlowEdge>, zone_to_id: &HashMap<String, usize>, old_assoc : &Vec< Vec<usize> >) -> Result<(), String > {
+        let mut cost = CostFunction::new();
+        for p in 0..NB_PARTITIONS {
+            for n in old_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);
+            }
+        }
+        let nb_nodes = self.useful_nodes().len();
+        let path_length = 4*nb_nodes;
+        gflow.optimize_flow_with_cost(&cost, path_length)?;
+
+        return Ok(());
+    }
+
+    fn update_ring_from_flow(&mut self, nb_zones : usize, gflow: &Graph<FlowEdge> ) -> Result<(), String>{
+        self.ring_assignation_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() {
+                    match vertex{
+                        Vertex::N(n) => self.ring_assignation_data.push((*n).try_into().unwrap()),
+                        _ => ()
+                    }
+                }
+            }
+        }
+
+        if self.ring_assignation_data.len() != NB_PARTITIONS*self.replication_factor {
+            return Err("Critical Error : the association ring we produced does not have the right size.".to_string());
+        }
+        return Ok(());
+    }
+    
+
+    //This function returns a message summing up the partition repartition of the new
+    //layout.
+    fn output_stat(&self , gflow : &Graph<FlowEdge>, 
+                    old_assoc_opt : &Option< Vec<Vec<usize>> >,
+                    zone_to_id: &HashMap<String, usize>, 
+                    id_to_zone : &Vec<String>) -> Result<Message, String>{
+        let mut msg = Message::new();
+        
+		let nb_partitions = 1usize << PARTITION_BITS;
+        let used_cap = self.partition_size * nb_partitions as u32 * 
+                self.replication_factor as u32;
+        let total_cap = self.get_total_capacity()?;
+        let percent_cap = 100.0*(used_cap as f32)/(total_cap as f32);
+        msg.push(format!("Available capacity / Total cluster capacity: {} / {} ({:.1} %)",
+            used_cap , total_cap , percent_cap ));
+        msg.push(format!("If the percentage is to low, it might be that the replication/redundancy constraints force the use of nodes/zones with small storage capacities. 
+        You might want to rebalance the storage capacities or relax the constraints. See the detailed statistics below and look for saturated nodes/zones."));
+        msg.push(format!("Recall that because of the replication, the actual available storage capacity is {} / {} = {}.", used_cap , self.replication_factor , used_cap/self.replication_factor as u32));
+       
+        //We define and fill in the following tables
+        let storing_nodes = self.useful_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.len() > 0 {
+                    stored_partitions_zone[z] += 1;
+                }
+                for vert in pz_nodes.iter() {
+                    if let Vertex::N(n) = *vert {
+                        stored_partitions[n] += 1;
+                        if let Some(old_assoc) = old_assoc_opt {
+                            if !old_assoc[p].contains(&n) {
+                                new_partitions[n] += 1;
+                            }
+                        }
+                    }
+                }
+                if let Some(old_assoc) = old_assoc_opt {
+                    let mut old_zones_of_p = Vec::<usize>::new();
+                    for n in old_assoc[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;
+                    }
+                }
+            }
+        }
+        
+        //We display the statistics
+
+        if *old_assoc_opt != None {
+            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(format!(""));
+        msg.push(format!("Detailed statistics by zones and nodes."));
+        
+        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();
+            msg.push(format!(""));
+            
+            if *old_assoc_opt != None {
+                msg.push(format!("Zone {}: {} distinct partitions stored ({} new, \
+                {} partition copies) ", id_to_zone[z], stored_partitions_zone[z], 
+                                 new_partitions_zone[z], replicated_partitions));
+            }
+            else{
+                msg.push(format!("Zone {}: {} distinct partitions stored ({} partition \
+                    copies) ", 
+                    id_to_zone[z], stored_partitions_zone[z], replicated_partitions));
+            }
+            
+            let available_cap_z : u32 = self.partition_size*replicated_partitions as u32;
+            let mut total_cap_z = 0;
+            for n in nodes_of_z.iter() {
+                total_cap_z += self.get_node_capacity(&self.node_id_vec[*n])?;
+            }
+            let percent_cap_z = 100.0*(available_cap_z as f32)/(total_cap_z as f32);
+            msg.push(format!("        Available capacity / Total capacity: {}/{} ({:.1}%).",
+                available_cap_z, total_cap_z, percent_cap_z));
+            msg.push(format!(""));
+            
+            for n in nodes_of_z.iter() {
+                let available_cap_n = stored_partitions[*n] as u32 *self.partition_size;
+                let total_cap_n =self.get_node_capacity(&self.node_id_vec[*n])?;
+                let tags_n = (self.node_role(&self.node_id_vec[*n])
+                                .ok_or("Node not found."))?.tags_string();
+                msg.push(format!("        Node {}: {} partitions ({} new) ; \
+                                 available/total capacity: {} / {} ({:.1}%) ; tags:{}", 
+                        &self.node_id_vec[*n].to_vec().encode_hex::<String>(), 
+                        stored_partitions[*n], 
+                        new_partitions[*n], available_cap_n, total_cap_n,
+                        (available_cap_n as f32)/(total_cap_n as f32)*100.0 ,
+                        tags_n));
+            }
+        }
+
+        return Ok(msg);
+    }
+    
 }
 
+//====================================================================================
+
 #[cfg(test)]
 mod tests {
 	use super::*;