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, 440 insertions, 0 deletions

diff --git a/src/rpc/graph_algo.rs b/src/rpc/graph_algo.rs
new file mode 100644
index 00000000..1a809b80
--- /dev/null
+++ b/src/rpc/graph_algo.rs
@@ -0,0 +1,440 @@
+
+//! This module deals with graph algorithms.
+//! It is used in layout.rs to build the partition to node assignation.
+
+use rand::prelude::SliceRandom;
+use std::cmp::{max, min};
+use std::collections::VecDeque;
+use std::collections::HashMap;
+
+//Vertex data structures used in all the graphs used in layout.rs.
+//usize parameters correspond to node/zone/partitions ids.
+//To understand the vertex roles below, please refer to the formal description
+//of the layout computation algorithm.
+#[derive(Clone,Copy,Debug, PartialEq, Eq, Hash)]
+pub enum Vertex{
+    Source,
+    Pup(usize),         //The vertex p+ of partition p
+    Pdown(usize),       //The vertex p- of partition p
+    PZ(usize,usize),    //The vertex corresponding to x_(partition p, zone z)
+    N(usize),           //The vertex corresponding to node n
+    Sink
+}
+
+
+//Edge data structure for the flow algorithm.
+//The graph is stored as an adjacency list
+#[derive(Clone, Copy, Debug)]
+pub struct FlowEdge {
+	cap: u32,     //flow maximal capacity of the edge
+	flow: i32,  //flow value on the edge
+	dest: usize,  //destination vertex id  
+	rev: usize, //index of the reversed edge (v, self) in the edge list of vertex v
+}
+
+//Edge data structure for the detection of negative cycles.
+//The graph is stored as a list of edges (u,v).
+#[derive(Clone, Copy, Debug)]
+pub struct WeightedEdge {
+	w: i32,     //weight of the edge
+	dest: usize,
+}
+
+pub trait Edge: Clone + Copy {}
+impl Edge for FlowEdge {}
+impl Edge for WeightedEdge {}
+
+//Struct for the graph structure. We do encapsulation here to be able to both
+//provide user friendly Vertex enum to address vertices, and to use usize indices
+//and Vec instead of HashMap in the graph algorithm to optimize execution speed.
+pub struct Graph<E : Edge>{
+    vertextoid : HashMap<Vertex , usize>,
+    idtovertex : Vec<Vertex>,
+    
+    graph : Vec< Vec<E> >
+}
+
+pub type CostFunction = HashMap<(Vertex,Vertex), i32>;
+
+impl<E : Edge> Graph<E>{
+    pub fn new(vertices : &[Vertex]) -> Self {
+        let mut map = HashMap::<Vertex, usize>::new();
+        for i in 0..vertices.len() {
+            map.insert(vertices[i] , i);
+        }
+        return Graph::<E> {
+                vertextoid : map,
+                idtovertex: vertices.to_vec(),
+                graph : vec![Vec::< E >::new(); vertices.len() ]
+            }
+    }
+}
+
+impl Graph<FlowEdge>{
+    //This function adds a directed edge to the graph with capacity c, and the
+    //corresponding reversed edge with capacity 0.
+    pub fn add_edge(&mut self, u: Vertex, v:Vertex, c: u32) -> Result<(), String>{
+        if !self.vertextoid.contains_key(&u) || !self.vertextoid.contains_key(&v) {
+            return Err("The graph does not contain the provided vertex.".to_string());
+        }
+        let idu = self.vertextoid[&u];
+        let idv = self.vertextoid[&v];
+        let rev_u = self.graph[idu].len();
+        let rev_v = self.graph[idv].len();
+        self.graph[idu].push( FlowEdge{cap: c , dest: idv , flow: 0, rev : rev_v} );
+        self.graph[idv].push( FlowEdge{cap: 0 , dest: idu , flow: 0, rev : rev_u} );
+        Ok(())
+    }
+    
+    //This function returns the list of vertices that receive a positive flow from
+    //vertex v.
+    pub fn get_positive_flow_from(&self , v:Vertex) -> Result< Vec<Vertex> , String>{
+        if !self.vertextoid.contains_key(&v) {
+            return Err("The graph does not contain the provided vertex.".to_string());
+        }
+        let idv = self.vertextoid[&v];
+        let mut result = Vec::<Vertex>::new();
+        for edge in self.graph[idv].iter() {
+            if edge.flow > 0 {
+                result.push(self.idtovertex[edge.dest]);
+            }
+        }
+        return Ok(result);
+    }
+    
+    
+    //This function returns the value of the flow incoming to v.
+    pub fn get_inflow(&self , v:Vertex) -> Result< i32 , String>{
+        if !self.vertextoid.contains_key(&v) {
+            return Err("The graph does not contain the provided vertex.".to_string());
+        }
+        let idv = self.vertextoid[&v];
+        let mut result = 0;
+        for edge in self.graph[idv].iter() {
+            result += max(0,self.graph[edge.dest][edge.rev].flow);
+        }
+        return Ok(result);
+    }
+
+    //This function returns the value of the flow outgoing from v.
+    pub fn get_outflow(&self , v:Vertex) -> Result< i32 , String>{
+        if !self.vertextoid.contains_key(&v) {
+            return Err("The graph does not contain the provided vertex.".to_string());
+        }
+        let idv = self.vertextoid[&v];
+        let mut result = 0;
+        for edge in self.graph[idv].iter() {
+            result += max(0,edge.flow);
+        }
+        return Ok(result);
+    }
+
+    //This function computes the flow total value by computing the outgoing flow
+    //from the source.
+    pub fn get_flow_value(&mut self) -> Result<i32, String> {
+        return self.get_outflow(Vertex::Source);
+    }
+
+    //This function shuffles the order of the edge lists. It keeps the ids of the
+    //reversed edges consistent.
+    fn shuffle_edges(&mut self) {
+        let mut rng = rand::thread_rng();
+        for i in 0..self.graph.len() {
+            self.graph[i].shuffle(&mut rng);
+            //We need to update the ids of the reverse edges.
+            for j in 0..self.graph[i].len() {
+                let target_v = self.graph[i][j].dest;
+                let target_rev = self.graph[i][j].rev;
+                self.graph[target_v][target_rev].rev = j;
+            }
+        }
+    }
+
+    //Computes an upper bound of the flow n the graph
+    pub fn flow_upper_bound(&self) -> u32{
+        let idsource = self.vertextoid[&Vertex::Source];
+        let mut flow_upper_bound = 0;
+        for edge in self.graph[idsource].iter(){
+            flow_upper_bound += edge.cap;
+        }
+        return flow_upper_bound;
+    }
+    
+    //This function computes the maximal flow using Dinic's algorithm. It starts with
+    //the flow values already present in the graph. So it is possible to add some edge to
+    //the graph, compute a flow, add other edges, update the flow.
+    pub fn compute_maximal_flow(&mut self) -> Result<(), String> {
+        if !self.vertextoid.contains_key(&Vertex::Source) { 
+            return Err("The graph does not contain a source.".to_string());
+        }
+        if !self.vertextoid.contains_key(&Vertex::Sink) { 
+            return Err("The graph does not contain a sink.".to_string());
+        }
+
+        let idsource = self.vertextoid[&Vertex::Source];
+        let idsink = self.vertextoid[&Vertex::Sink];
+       
+        let nb_vertices = self.graph.len();
+
+        let flow_upper_bound = self.flow_upper_bound();
+        
+        //To ensure the dispersion of the associations generated by the
+        //assignation, we shuffle the neighbours of the nodes. Hence,
+        //the vertices do not consider their neighbours in the same order.
+        self.shuffle_edges();
+
+        //We run Dinic's max flow algorithm
+        loop {
+            //We build the level array from Dinic's algorithm.
+            let mut level = vec![None; nb_vertices];
+
+            let mut fifo = VecDeque::new();
+            fifo.push_back((idsource, 0));
+            while !fifo.is_empty() {
+                if let Some((id, lvl)) = fifo.pop_front() {
+                    if level[id] == None {  //it means id has not yet been reached
+                        level[id] = Some(lvl);
+                        for edge in self.graph[id].iter() {
+                            if edge.cap as i32 - edge.flow > 0 {
+                                fifo.push_back((edge.dest, lvl + 1));
+                            }
+                        }
+                    }
+                }
+            }
+            if level[idsink] == None {
+                //There is no residual flow
+                break;
+            }
+
+            //Now we run DFS respecting the level array
+            let mut next_nbd = vec![0; nb_vertices];
+            let mut lifo = VecDeque::new();
+
+            lifo.push_back((idsource, flow_upper_bound));
+
+            while let Some((id_tmp, f_tmp)) = lifo.back() {
+                let id = *id_tmp;
+                let f = *f_tmp;
+                if id == idsink {
+                    //The DFS reached the sink, we can add a
+                    //residual flow.
+                    lifo.pop_back();
+                    while !lifo.is_empty() {
+                        if let Some((id, _)) = lifo.pop_back() {
+                            let nbd = next_nbd[id];
+                            self.graph[id][nbd].flow += f as i32;
+                            let id_rev = self.graph[id][nbd].dest;
+                            let nbd_rev = self.graph[id][nbd].rev;
+                            self.graph[id_rev][nbd_rev].flow -= f as i32;
+                        }
+                    }
+                    lifo.push_back((idsource, flow_upper_bound));
+                    continue;
+                }
+                //else we did not reach the sink
+                let nbd = next_nbd[id];
+                if nbd >= self.graph[id].len() {
+                    //There is nothing to explore from id anymore
+                    lifo.pop_back();
+                    if let Some((parent, _)) = lifo.back() {
+                        next_nbd[*parent] += 1;
+                    }
+                    continue;
+                }
+                //else we can try to send flow from id to its nbd
+                let new_flow = min(f, self.graph[id][nbd].cap - self.graph[id][nbd].flow as u32 );
+                if let (Some(lvldest), Some(lvlid)) =
+                                (level[self.graph[id][nbd].dest], level[id]){
+                    if lvldest <= lvlid || new_flow == 0 {
+                        //We cannot send flow to nbd.
+                        next_nbd[id] += 1;
+                        continue;
+                    }
+                }
+                //otherwise, we send flow to nbd.
+                lifo.push_back((self.graph[id][nbd].dest, new_flow));
+            }
+        }
+        Ok(())
+    }
+
+    //This function takes a flow, and a cost function on the edges, and tries to find an
+    // equivalent flow with a better cost, by finding improving overflow cycles. It uses 
+    // as subroutine the Bellman Ford algorithm run up to path_length.
+    // We assume that the cost of edge (u,v) is the opposite of the cost of (v,u), and only
+    // one needs to be present in the cost function.
+    pub fn optimize_flow_with_cost(&mut self , cost: &CostFunction, path_length: usize )
+        -> Result<(),String>{
+        
+        //We build the weighted graph g where we will look for negative cycle
+        let mut gf = self.build_cost_graph(cost)?;
+        let mut cycles = gf.list_negative_cycles(path_length);
+        while cycles.len() > 0 {
+            //we enumerate negative cycles
+            for c in cycles.iter(){
+                for i in 0..c.len(){
+                    //We add one flow unit to the edge (u,v) of cycle c
+                    let idu = self.vertextoid[&c[i]];
+                    let idv = self.vertextoid[&c[(i+1)%c.len()]];
+                    for j in 0..self.graph[idu].len(){
+                        //since idu appears at most once in the cycles, we enumerate every
+                        //edge at most once.
+                        let edge = self.graph[idu][j];
+                        if edge.dest == idv {
+                            self.graph[idu][j].flow += 1;
+                            self.graph[idv][edge.rev].flow -=1;
+                            break;
+                        }
+                    }
+                }
+            }
+
+            gf = self.build_cost_graph(cost)?;
+            cycles = gf.list_negative_cycles(path_length);
+        }
+        return Ok(());
+    }
+
+    //Construct the weighted graph G_f from the flow and the cost function
+    fn build_cost_graph(&self , cost: &CostFunction) -> Result<Graph<WeightedEdge>,String>{
+        
+        let mut g = Graph::<WeightedEdge>::new(&self.idtovertex);
+        let nb_vertices = self.idtovertex.len();
+        for i in 0..nb_vertices {
+            for edge in self.graph[i].iter() {
+                if edge.cap as  i32 -edge.flow > 0 {
+                    //It is possible to send overflow through this edge
+                    let u = self.idtovertex[i];
+                    let v = self.idtovertex[edge.dest];
+                    if cost.contains_key(&(u,v)) {
+                        g.add_edge(u,v, cost[&(u,v)])?;
+                    }
+                    else if cost.contains_key(&(v,u)) {
+                        g.add_edge(u,v, -cost[&(v,u)])?;
+                    }
+                    else{
+                        g.add_edge(u,v, 0)?;
+                    }
+                }
+            }
+        }
+        return Ok(g);
+
+    }
+
+
+}
+
+impl Graph<WeightedEdge>{
+    //This function adds a single directed weighted edge to the graph.
+    pub fn add_edge(&mut self, u: Vertex, v:Vertex, w: i32) -> Result<(), String>{
+        if !self.vertextoid.contains_key(&u) || !self.vertextoid.contains_key(&v) {
+            return Err("The graph does not contain the provided vertex.".to_string());
+        }
+        let idu = self.vertextoid[&u];
+        let idv = self.vertextoid[&v];
+        self.graph[idu].push( WeightedEdge{w: w , dest: idv} );
+        Ok(())
+    }
+
+    //This function lists the negative cycles it manages to find after path_length
+    //iterations of the main loop of the Bellman-Ford algorithm. For the classical
+    //algorithm, path_length needs to be equal to the number of vertices. However, 
+    //for particular graph structures like our case, the algorithm is still correct
+    //when path_length is the length of the longest possible simple path. 
+    //See the formal description of the algorithm for more details. 
+    fn list_negative_cycles(&self, path_length: usize) -> Vec< Vec<Vertex> > {
+        
+        let nb_vertices = self.graph.len();
+        
+        //We start with every vertex at distance 0 of some imaginary extra -1 vertex.
+        let mut distance = vec![0 ; nb_vertices];
+        //The prev vector collects for every vertex from where does the shortest path come
+        let mut prev = vec![None; nb_vertices];
+
+        for _ in 0..path_length +1 {
+            for id in 0..nb_vertices{
+                for e in self.graph[id].iter(){
+                    if distance[id] + e.w < distance[e.dest] {
+                        distance[e.dest] = distance[id] + e.w;
+                        prev[e.dest] = Some(id);
+                    }
+                }
+            }
+        }
+
+        //If self.graph contains a negative cycle, then at this point the graph described
+        //by prev (which is a directed 1-forest/functional graph) 
+        //must contain a cycle. We list the cycles of prev.
+        let cycles_prev = cycles_of_1_forest(&prev);
+
+        //Remark that the cycle in prev is in the reverse order compared to the cycle
+        //in the graph. Thus the .rev().
+        return cycles_prev.iter().map(|cycle| cycle.iter().rev().map(
+                |id| self.idtovertex[*id]
+                    ).collect() ).collect();
+    }
+
+}
+
+
+//This function returns the list of cycles of a directed 1 forest. It does not
+//check for the consistency of the input.
+fn cycles_of_1_forest(forest: &[Option<usize>])  -> Vec<Vec<usize>> {
+    let mut cycles = Vec::<Vec::<usize>>::new();
+    let mut time_of_discovery = vec![None; forest.len()];
+
+    for t in 0..forest.len(){
+        let mut id = t;
+        //while we are on a valid undiscovered node
+        while time_of_discovery[id] == None {
+            time_of_discovery[id] = Some(t);
+            if let Some(i) = forest[id] {
+                id = i;
+            }
+            else{
+                break;
+            }
+        }
+        if forest[id] != None && time_of_discovery[id] == Some(t) {
+            //We discovered an id that we explored at this iteration t.
+            //It means we are on a cycle
+            let mut cy = vec![id; 1];
+            let id2 = id;
+            while let Some(id2) = forest[id2] {
+                if id2 != id {
+                    cy.push(id2);
+                }
+                else {
+                    break;
+                }
+            }
+            cycles.push(cy);
+        }
+    }
+    return cycles;
+}
+
+
+//====================================================================================
+//====================================================================================
+//====================================================================================
+//====================================================================================
+//====================================================================================
+//====================================================================================
+
+
+#[cfg(test)]
+mod tests {
+	use super::*;
+
+	#[test]
+	fn test_flow() {
+		let left_vec = vec![3; 8];
+		let right_vec = vec![0, 4, 8, 4, 8];
+		//There are asserts in the function that computes the flow
+	}
+
+	//maybe add tests relative to the matching optilization ?
+}