From 7f3249a23770fd4da981c2ecb1126da97e9b4ca5 Mon Sep 17 00:00:00 2001 From: Mendes Date: Wed, 21 Sep 2022 14:39:59 +0200 Subject: 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 --- src/rpc/graph_algo.rs | 440 ++++++++++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 440 insertions(+) create mode 100644 src/rpc/graph_algo.rs (limited to 'src/rpc/graph_algo.rs') 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{ + vertextoid : HashMap, + idtovertex : Vec, + + graph : Vec< Vec > +} + +pub type CostFunction = HashMap<(Vertex,Vertex), i32>; + +impl Graph{ + pub fn new(vertices : &[Vertex]) -> Self { + let mut map = HashMap::::new(); + for i in 0..vertices.len() { + map.insert(vertices[i] , i); + } + return Graph:: { + vertextoid : map, + idtovertex: vertices.to_vec(), + graph : vec![Vec::< E >::new(); vertices.len() ] + } + } +} + +impl Graph{ + //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 , 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::::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 { + 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,String>{ + + let mut g = Graph::::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{ + //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 > { + + 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]) -> Vec> { + let mut cycles = Vec::>::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 ? +} -- cgit v1.2.3 From bd842e1388a324e2a3956465e9b32d0dc739a8d9 Mon Sep 17 00:00:00 2001 From: Mendes Date: Thu, 22 Sep 2022 19:30:01 +0200 Subject: Correction of a few bugs in the tests, modification of ClusterLayout::check --- src/rpc/graph_algo.rs | 41 ++++++++++++++++++----------------------- 1 file changed, 18 insertions(+), 23 deletions(-) (limited to 'src/rpc/graph_algo.rs') diff --git a/src/rpc/graph_algo.rs b/src/rpc/graph_algo.rs index 1a809b80..a5a1e4ba 100644 --- a/src/rpc/graph_algo.rs +++ b/src/rpc/graph_algo.rs @@ -182,7 +182,7 @@ impl Graph{ //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. @@ -206,7 +206,6 @@ impl Graph{ //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(); @@ -220,14 +219,12 @@ impl Graph{ //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; - } + while 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; @@ -243,10 +240,14 @@ impl Graph{ 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 ); + let new_flow = min(f as i32, self.graph[id][nbd].cap as i32 - self.graph[id][nbd].flow) as u32; + if new_flow == 0 { + next_nbd[id] += 1; + continue; + } if let (Some(lvldest), Some(lvlid)) = (level[self.graph[id][nbd].dest], level[id]){ - if lvldest <= lvlid || new_flow == 0 { + if lvldest <= lvlid { //We cannot send flow to nbd. next_nbd[id] += 1; continue; @@ -266,7 +267,6 @@ impl Graph{ // 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); @@ -364,6 +364,7 @@ impl Graph{ } } + //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. @@ -401,8 +402,9 @@ fn cycles_of_1_forest(forest: &[Option]) -> Vec> { //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] { + let mut id2 = id; + while let Some(id_next) = forest[id2] { + id2 = id_next; if id2 != id { cy.push(id2); } @@ -429,12 +431,5 @@ fn cycles_of_1_forest(forest: &[Option]) -> Vec> { 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 ? } + -- cgit v1.2.3 From 911eb17bd9e25f2f02fbe1de81a3384e99ea13ac Mon Sep 17 00:00:00 2001 From: Mendes Date: Thu, 6 Oct 2022 14:53:57 +0200 Subject: corrected warnings of cargo clippy --- src/rpc/graph_algo.rs | 26 +++++++++++++------------- 1 file changed, 13 insertions(+), 13 deletions(-) (limited to 'src/rpc/graph_algo.rs') diff --git a/src/rpc/graph_algo.rs b/src/rpc/graph_algo.rs index a5a1e4ba..4e27631a 100644 --- a/src/rpc/graph_algo.rs +++ b/src/rpc/graph_algo.rs @@ -59,10 +59,10 @@ pub type CostFunction = HashMap<(Vertex,Vertex), i32>; impl Graph{ pub fn new(vertices : &[Vertex]) -> Self { let mut map = HashMap::::new(); - for i in 0..vertices.len() { - map.insert(vertices[i] , i); + for (i, vert) in vertices.iter().enumerate(){ + map.insert(*vert , i); } - return Graph:: { + Graph:: { vertextoid : map, idtovertex: vertices.to_vec(), graph : vec![Vec::< E >::new(); vertices.len() ] @@ -99,7 +99,7 @@ impl Graph{ result.push(self.idtovertex[edge.dest]); } } - return Ok(result); + Ok(result) } @@ -113,7 +113,7 @@ impl Graph{ for edge in self.graph[idv].iter() { result += max(0,self.graph[edge.dest][edge.rev].flow); } - return Ok(result); + Ok(result) } //This function returns the value of the flow outgoing from v. @@ -126,13 +126,13 @@ impl Graph{ for edge in self.graph[idv].iter() { result += max(0,edge.flow); } - return Ok(result); + 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 { - return self.get_outflow(Vertex::Source); + self.get_outflow(Vertex::Source) } //This function shuffles the order of the edge lists. It keeps the ids of the @@ -157,7 +157,7 @@ impl Graph{ for edge in self.graph[idsource].iter(){ flow_upper_bound += edge.cap; } - return flow_upper_bound; + flow_upper_bound } //This function computes the maximal flow using Dinic's algorithm. It starts with @@ -270,7 +270,7 @@ impl Graph{ //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 { + while !cycles.is_empty() { //we enumerate negative cycles for c in cycles.iter(){ for i in 0..c.len(){ @@ -293,7 +293,7 @@ impl Graph{ gf = self.build_cost_graph(cost)?; cycles = gf.list_negative_cycles(path_length); } - return Ok(()); + Ok(()) } //Construct the weighted graph G_f from the flow and the cost function @@ -319,7 +319,7 @@ impl Graph{ } } } - return Ok(g); + Ok(g) } @@ -334,7 +334,7 @@ impl Graph{ } let idu = self.vertextoid[&u]; let idv = self.vertextoid[&v]; - self.graph[idu].push( WeightedEdge{w: w , dest: idv} ); + self.graph[idu].push( WeightedEdge{ w , dest: idv} ); Ok(()) } @@ -415,7 +415,7 @@ fn cycles_of_1_forest(forest: &[Option]) -> Vec> { cycles.push(cy); } } - return cycles; + cycles } -- cgit v1.2.3 From fcf9ac674a2842b2b55d933e60af5af93dcc4592 Mon Sep 17 00:00:00 2001 From: Mendes Date: Mon, 10 Oct 2022 17:19:25 +0200 Subject: Tests written in layout.rs added staged_parameters to ClusterLayout removed the serde(default) -> will need a migration function --- src/rpc/graph_algo.rs | 14 -------------- 1 file changed, 14 deletions(-) (limited to 'src/rpc/graph_algo.rs') diff --git a/src/rpc/graph_algo.rs b/src/rpc/graph_algo.rs index 4e27631a..70ccf35a 100644 --- a/src/rpc/graph_algo.rs +++ b/src/rpc/graph_algo.rs @@ -419,17 +419,3 @@ fn cycles_of_1_forest(forest: &[Option]) -> Vec> { } -//==================================================================================== -//==================================================================================== -//==================================================================================== -//==================================================================================== -//==================================================================================== -//==================================================================================== - - -#[cfg(test)] -mod tests { - use super::*; - -} - -- cgit v1.2.3 From 4abab246f1113a9a1988fdfca81c1dd8ffa323c8 Mon Sep 17 00:00:00 2001 From: Mendes Date: Mon, 10 Oct 2022 17:21:13 +0200 Subject: cargo fmt --- src/rpc/graph_algo.rs | 754 +++++++++++++++++++++++++------------------------- 1 file changed, 377 insertions(+), 377 deletions(-) (limited to 'src/rpc/graph_algo.rs') diff --git a/src/rpc/graph_algo.rs b/src/rpc/graph_algo.rs index 70ccf35a..13c60692 100644 --- a/src/rpc/graph_algo.rs +++ b/src/rpc/graph_algo.rs @@ -1,42 +1,40 @@ - //! 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; +use std::collections::VecDeque; //Vertex data structures used in all the graphs used in layout.rs. //usize parameters correspond to node/zone/partitions ids. //To understand the vertex roles below, please refer to the formal description //of the layout computation algorithm. -#[derive(Clone,Copy,Debug, PartialEq, Eq, Hash)] -pub enum Vertex{ - Source, - Pup(usize), //The vertex p+ of partition p - Pdown(usize), //The vertex p- of partition p - PZ(usize,usize), //The vertex corresponding to x_(partition p, zone z) - N(usize), //The vertex corresponding to node n - Sink +#[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 + 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 + w: i32, //weight of the edge dest: usize, } @@ -47,375 +45,377 @@ 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{ - vertextoid : HashMap, - idtovertex : Vec, - - graph : Vec< Vec > -} +pub struct Graph { + vertextoid: HashMap, + idtovertex: Vec, -pub type CostFunction = HashMap<(Vertex,Vertex), i32>; - -impl Graph{ - pub fn new(vertices : &[Vertex]) -> Self { - let mut map = HashMap::::new(); - for (i, vert) in vertices.iter().enumerate(){ - map.insert(*vert , i); - } - Graph:: { - vertextoid : map, - idtovertex: vertices.to_vec(), - graph : vec![Vec::< E >::new(); vertices.len() ] - } - } + graph: Vec>, } -impl Graph{ - //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 , 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::::new(); - for edge in self.graph[idv].iter() { - if edge.flow > 0 { - result.push(self.idtovertex[edge.dest]); - } - } - 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); - } - 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); - } - 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 { - 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; - } - 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 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 as i32, self.graph[id][nbd].cap as i32 - self.graph[id][nbd].flow) as u32; - if new_flow == 0 { - next_nbd[id] += 1; - continue; - } - if let (Some(lvldest), Some(lvlid)) = - (level[self.graph[id][nbd].dest], level[id]){ - if lvldest <= lvlid { - //We cannot send flow to nbd. - next_nbd[id] += 1; - continue; - } - } - //otherwise, we send flow to nbd. - lifo.push_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.is_empty() { - //we enumerate negative cycles - for c in cycles.iter(){ - for i in 0..c.len(){ - //We add one flow unit to the edge (u,v) of cycle c - let idu = self.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); - } - Ok(()) - } - - //Construct the weighted graph G_f from the flow and the cost function - fn build_cost_graph(&self , cost: &CostFunction) -> Result,String>{ - - let mut g = Graph::::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)?; - } - } - } - } - Ok(g) - - } - - +pub type CostFunction = HashMap<(Vertex, Vertex), i32>; + +impl Graph { + pub fn new(vertices: &[Vertex]) -> Self { + let mut map = HashMap::::new(); + for (i, vert) in vertices.iter().enumerate() { + map.insert(*vert, i); + } + Graph:: { + vertextoid: map, + idtovertex: vertices.to_vec(), + graph: vec![Vec::::new(); vertices.len()], + } + } } -impl Graph{ - //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 , 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 > { - - 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(); - } - +impl Graph { + //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, 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::::new(); + for edge in self.graph[idv].iter() { + if edge.flow > 0 { + result.push(self.idtovertex[edge.dest]); + } + } + Ok(result) + } + + //This function returns the value of the flow incoming to v. + pub fn get_inflow(&self, v: Vertex) -> Result { + 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); + } + Ok(result) + } + + //This function returns the value of the flow outgoing from v. + pub fn get_outflow(&self, v: Vertex) -> Result { + 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); + } + 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 { + 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; + } + 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 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 as i32, + self.graph[id][nbd].cap as i32 - self.graph[id][nbd].flow, + ) as u32; + if new_flow == 0 { + next_nbd[id] += 1; + continue; + } + if let (Some(lvldest), Some(lvlid)) = (level[self.graph[id][nbd].dest], level[id]) { + if lvldest <= lvlid { + //We cannot send flow to nbd. + next_nbd[id] += 1; + continue; + } + } + //otherwise, we send flow to nbd. + lifo.push_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.is_empty() { + //we enumerate negative cycles + for c in cycles.iter() { + for i in 0..c.len() { + //We add one flow unit to the edge (u,v) of cycle c + let idu = self.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); + } + Ok(()) + } + + //Construct the weighted graph G_f from the flow and the cost function + fn build_cost_graph(&self, cost: &CostFunction) -> Result, String> { + let mut g = Graph::::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)?; + } + } + } + } + Ok(g) + } } +impl Graph { + //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, 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> { + 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]) -> Vec> { - let mut cycles = Vec::>::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 mut id2 = id; - while let Some(id_next) = forest[id2] { - id2 = id_next; - if id2 != id { - cy.push(id2); - } - else { - break; - } - } - cycles.push(cy); - } - } - cycles +fn cycles_of_1_forest(forest: &[Option]) -> Vec> { + let mut cycles = Vec::>::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 mut id2 = id; + while let Some(id_next) = forest[id2] { + id2 = id_next; + if id2 != id { + cy.push(id2); + } else { + break; + } + } + cycles.push(cy); + } + } + cycles } - - -- cgit v1.2.3 From bcdd1e0c3335500a6d0337ce6ee050fb59fc665a Mon Sep 17 00:00:00 2001 From: Mendes Date: Tue, 11 Oct 2022 18:29:21 +0200 Subject: Added some comment --- src/rpc/graph_algo.rs | 79 +++++++++++++++++++++++++-------------------------- 1 file changed, 39 insertions(+), 40 deletions(-) (limited to 'src/rpc/graph_algo.rs') diff --git a/src/rpc/graph_algo.rs b/src/rpc/graph_algo.rs index 13c60692..5bd6cc51 100644 --- a/src/rpc/graph_algo.rs +++ b/src/rpc/graph_algo.rs @@ -6,10 +6,10 @@ use std::cmp::{max, min}; use std::collections::HashMap; use std::collections::VecDeque; -//Vertex data structures used in all the graphs used in layout.rs. -//usize parameters correspond to node/zone/partitions ids. -//To understand the vertex roles below, please refer to the formal description -//of the layout computation algorithm. +///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, @@ -20,8 +20,7 @@ pub enum Vertex { Sink, } -//Edge data structure for the flow algorithm. -//The graph is stored as an adjacency list +///Edge data structure for the flow algorithm. #[derive(Clone, Copy, Debug)] pub struct FlowEdge { cap: u32, //flow maximal capacity of the edge @@ -30,8 +29,7 @@ pub struct FlowEdge { 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). +///Edge data structure for the detection of negative cycles. #[derive(Clone, Copy, Debug)] pub struct WeightedEdge { w: i32, //weight of the edge @@ -42,13 +40,14 @@ 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. +///Struct for the graph structure. We do encapsulation here to be able to both +///provide user friendly Vertex enum to address vertices, and to use internally usize +///indices and Vec instead of HashMap in the graph algorithm to optimize execution speed. pub struct Graph { vertextoid: HashMap, idtovertex: Vec, + //The graph is stored as an adjacency list graph: Vec>, } @@ -69,8 +68,8 @@ impl Graph { } impl Graph { - //This function adds a directed edge to the graph with capacity c, and the - //corresponding reversed edge with capacity 0. + ///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()); @@ -94,8 +93,8 @@ impl Graph { Ok(()) } - //This function returns the list of vertices that receive a positive flow from - //vertex v. + ///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, String> { if !self.vertextoid.contains_key(&v) { return Err("The graph does not contain the provided vertex.".to_string()); @@ -110,7 +109,7 @@ impl Graph { Ok(result) } - //This function returns the value of the flow incoming to v. + ///This function returns the value of the flow incoming to v. pub fn get_inflow(&self, v: Vertex) -> Result { if !self.vertextoid.contains_key(&v) { return Err("The graph does not contain the provided vertex.".to_string()); @@ -123,7 +122,7 @@ impl Graph { Ok(result) } - //This function returns the value of the flow outgoing from v. + ///This function returns the value of the flow outgoing from v. pub fn get_outflow(&self, v: Vertex) -> Result { if !self.vertextoid.contains_key(&v) { return Err("The graph does not contain the provided vertex.".to_string()); @@ -136,14 +135,14 @@ impl Graph { Ok(result) } - //This function computes the flow total value by computing the outgoing flow - //from the source. + ///This function computes the flow total value by computing the outgoing flow + ///from the source. pub fn get_flow_value(&mut self) -> Result { self.get_outflow(Vertex::Source) } - //This function shuffles the order of the edge lists. It keeps the ids of the - //reversed edges consistent. + ///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() { @@ -157,7 +156,7 @@ impl Graph { } } - //Computes an upper bound of the flow n the graph + ///Computes an upper bound of the flow on the graph pub fn flow_upper_bound(&self) -> u32 { let idsource = self.vertextoid[&Vertex::Source]; let mut flow_upper_bound = 0; @@ -167,9 +166,9 @@ impl Graph { 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. + ///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()); @@ -270,11 +269,11 @@ impl Graph { 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. + ///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, @@ -309,7 +308,7 @@ impl Graph { Ok(()) } - //Construct the weighted graph G_f from the flow and the cost function + ///Construct the weighted graph G_f from the flow and the cost function fn build_cost_graph(&self, cost: &CostFunction) -> Result, String> { let mut g = Graph::::new(&self.idtovertex); let nb_vertices = self.idtovertex.len(); @@ -334,7 +333,7 @@ impl Graph { } impl Graph { - //This function adds a single directed weighted edge to the graph. + ///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()); @@ -345,12 +344,12 @@ impl Graph { 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. + ///This function lists the negative cycles it manages to find after path_length + ///iterations of the main loop of the Bellman-Ford algorithm. For the classical + ///algorithm, path_length needs to be equal to the number of vertices. However, + ///for particular graph structures like in our case, the algorithm is still correct + ///when path_length is the length of the longest possible simple path. + ///See the formal description of the algorithm for more details. fn list_negative_cycles(&self, path_length: usize) -> Vec> { let nb_vertices = self.graph.len(); @@ -384,8 +383,8 @@ impl Graph { } } -//This function returns the list of cycles of a directed 1 forest. It does not -//check for the consistency of the input. +///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]) -> Vec> { let mut cycles = Vec::>::new(); let mut time_of_discovery = vec![None; forest.len()]; -- cgit v1.2.3 From ea5afc251106b3f6e2d07f942ba1f88abeef8765 Mon Sep 17 00:00:00 2001 From: Alex Auvolat Date: Mon, 7 Nov 2022 19:34:40 +0100 Subject: Style improvements --- src/rpc/graph_algo.rs | 273 ++++++++++++++++++++++++-------------------------- 1 file changed, 132 insertions(+), 141 deletions(-) (limited to 'src/rpc/graph_algo.rs') diff --git a/src/rpc/graph_algo.rs b/src/rpc/graph_algo.rs index 5bd6cc51..1e4a819b 100644 --- a/src/rpc/graph_algo.rs +++ b/src/rpc/graph_algo.rs @@ -6,33 +6,33 @@ use std::cmp::{max, min}; use std::collections::HashMap; use std::collections::VecDeque; -///Vertex data structures used in all the graphs used in layout.rs. -///usize parameters correspond to node/zone/partitions ids. -///To understand the vertex roles below, please refer to the formal description -///of the layout computation algorithm. +/// 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 + 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. +/// Edge data structure for the flow algorithm. #[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 + 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. +/// Edge data structure for the detection of negative cycles. #[derive(Clone, Copy, Debug)] pub struct WeightedEdge { - w: i32, //weight of the edge + w: i32, // weight of the edge dest: usize, } @@ -40,14 +40,14 @@ pub trait Edge: Clone + Copy {} impl Edge for FlowEdge {} impl Edge for WeightedEdge {} -///Struct for the graph structure. We do encapsulation here to be able to both -///provide user friendly Vertex enum to address vertices, and to use internally usize -///indices and Vec instead of HashMap in the graph algorithm to optimize execution speed. +/// Struct for the graph structure. We do encapsulation here to be able to both +/// provide user friendly Vertex enum to address vertices, and to use internally usize +/// indices and Vec instead of HashMap in the graph algorithm to optimize execution speed. pub struct Graph { - vertextoid: HashMap, - idtovertex: Vec, + vertex_to_id: HashMap, + id_to_vertex: Vec, - //The graph is stored as an adjacency list + // The graph is stored as an adjacency list graph: Vec>, } @@ -60,22 +60,30 @@ impl Graph { map.insert(*vert, i); } Graph:: { - vertextoid: map, - idtovertex: vertices.to_vec(), + vertex_to_id: map, + id_to_vertex: vertices.to_vec(), graph: vec![Vec::::new(); vertices.len()], } } + + fn get_vertex_id(&self, v: &Vertex) -> Result { + self.vertex_to_id + .get(v) + .cloned() + .ok_or_else(|| format!("The graph does not contain vertex {:?}", v)) + } } impl Graph { - ///This function adds a directed edge to the graph with capacity c, and the - ///corresponding reversed edge with capacity 0. + /// 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.get_vertex_id(&u)?; + let idv = self.get_vertex_id(&v)?; + if idu == idv { + return Err("Cannot add edge from vertex to itself in flow graph".into()); } - let 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 { @@ -93,28 +101,22 @@ impl Graph { Ok(()) } - ///This function returns the list of vertices that receive a positive flow from - ///vertex v. + /// 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, 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 idv = self.get_vertex_id(&v)?; let mut result = Vec::::new(); for edge in self.graph[idv].iter() { if edge.flow > 0 { - result.push(self.idtovertex[edge.dest]); + result.push(self.id_to_vertex[edge.dest]); } } Ok(result) } - ///This function returns the value of the flow incoming to v. + /// This function returns the value of the flow incoming to v. pub fn get_inflow(&self, v: Vertex) -> Result { - if !self.vertextoid.contains_key(&v) { - return Err("The graph does not contain the provided vertex.".to_string()); - } - let idv = self.vertextoid[&v]; + let idv = self.get_vertex_id(&v)?; let mut result = 0; for edge in self.graph[idv].iter() { result += max(0, self.graph[edge.dest][edge.rev].flow); @@ -122,12 +124,9 @@ impl Graph { Ok(result) } - ///This function returns the value of the flow outgoing from v. + /// This function returns the value of the flow outgoing from v. pub fn get_outflow(&self, v: Vertex) -> Result { - if !self.vertextoid.contains_key(&v) { - return Err("The graph does not contain the provided vertex.".to_string()); - } - let idv = self.vertextoid[&v]; + let idv = self.get_vertex_id(&v)?; let mut result = 0; for edge in self.graph[idv].iter() { result += max(0, edge.flow); @@ -135,19 +134,19 @@ impl Graph { Ok(result) } - ///This function computes the flow total value by computing the outgoing flow - ///from the source. + /// This function computes the flow total value by computing the outgoing flow + /// from the source. pub fn get_flow_value(&mut self) -> Result { self.get_outflow(Vertex::Source) } - ///This function shuffles the order of the edge lists. It keeps the ids of the - ///reversed edges consistent. + /// 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. + // 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; @@ -156,97 +155,86 @@ impl Graph { } } - ///Computes an upper bound of the flow on the graph - pub fn flow_upper_bound(&self) -> u32 { - let idsource = self.vertextoid[&Vertex::Source]; + /// Computes an upper bound of the flow on the graph + pub fn flow_upper_bound(&self) -> Result { + let idsource = self.get_vertex_id(&Vertex::Source)?; let mut flow_upper_bound = 0; for edge in self.graph[idsource].iter() { flow_upper_bound += edge.cap; } - flow_upper_bound + Ok(flow_upper_bound) } - ///This function computes the maximal flow using Dinic's algorithm. It starts with - ///the flow values already present in the graph. So it is possible to add some edge to - ///the graph, compute a flow, add other edges, update the flow. + /// 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 idsource = self.get_vertex_id(&Vertex::Source)?; + let idsink = self.get_vertex_id(&Vertex::Sink)?; let nb_vertices = self.graph.len(); - let flow_upper_bound = self.flow_upper_bound(); + 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. + // 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 + // We run Dinic's max flow algorithm loop { - //We build the level array from Dinic's algorithm. + // 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)); - } + while 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 + // There is no residual flow break; } - //Now we run DFS respecting the level array + // Now we run DFS respecting the level array let mut next_nbd = vec![0; nb_vertices]; - let mut lifo = VecDeque::new(); + let mut lifo = Vec::new(); - lifo.push_back((idsource, flow_upper_bound)); + lifo.push((idsource, flow_upper_bound)); - while let Some((id_tmp, f_tmp)) = lifo.back() { - let id = *id_tmp; - let f = *f_tmp; + while let Some((id, f)) = lifo.last().cloned() { if id == idsink { - //The DFS reached the sink, we can add a - //residual flow. - lifo.pop_back(); - while let Some((id, _)) = lifo.pop_back() { + // The DFS reached the sink, we can add a + // residual flow. + lifo.pop(); + while let Some((id, _)) = lifo.pop() { let nbd = next_nbd[id]; self.graph[id][nbd].flow += f as 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)); + lifo.push((idsource, flow_upper_bound)); continue; } - //else we did not reach the sink + // 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() { + // There is nothing to explore from id anymore + lifo.pop(); + if let Some((parent, _)) = lifo.last() { next_nbd[*parent] += 1; } continue; } - //else we can try to send flow from id to its nbd + // else we can try to send flow from id to its nbd let new_flow = min( f as i32, self.graph[id][nbd].cap as i32 - self.graph[id][nbd].flow, @@ -257,19 +245,19 @@ impl Graph { } if let (Some(lvldest), Some(lvlid)) = (level[self.graph[id][nbd].dest], level[id]) { if lvldest <= lvlid { - //We cannot send flow to nbd. + // 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)); + // otherwise, we send flow to nbd. + lifo.push((self.graph[id][nbd].dest, new_flow)); } } Ok(()) } - ///This function takes a flow, and a cost function on the edges, and tries to find an + /// 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 @@ -279,19 +267,19 @@ impl Graph { cost: &CostFunction, path_length: usize, ) -> Result<(), String> { - //We build the weighted graph g where we will look for negative cycle + // We build the weighted graph g where we will look for negative cycle let mut gf = self.build_cost_graph(cost)?; let mut cycles = gf.list_negative_cycles(path_length); while !cycles.is_empty() { - //we enumerate negative cycles + // 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()]]; + // We add one flow unit to the edge (u,v) of cycle c + let idu = self.vertex_to_id[&c[i]]; + let idv = self.vertex_to_id[&c[(i + 1) % c.len()]]; for j in 0..self.graph[idu].len() { - //since idu appears at most once in the cycles, we enumerate every - //edge at most once. + // 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; @@ -308,16 +296,16 @@ impl Graph { Ok(()) } - ///Construct the weighted graph G_f from the flow and the cost function + /// Construct the weighted graph G_f from the flow and the cost function fn build_cost_graph(&self, cost: &CostFunction) -> Result, String> { - let mut g = Graph::::new(&self.idtovertex); - let nb_vertices = self.idtovertex.len(); + let mut g = Graph::::new(&self.id_to_vertex); + let nb_vertices = self.id_to_vertex.len(); for i in 0..nb_vertices { for edge in self.graph[i].iter() { if edge.cap as i32 - edge.flow > 0 { - //It is possible to send overflow through this edge - let u = self.idtovertex[i]; - let v = self.idtovertex[edge.dest]; + // It is possible to send overflow through this edge + let u = self.id_to_vertex[i]; + let v = self.id_to_vertex[edge.dest]; if cost.contains_key(&(u, v)) { g.add_edge(u, v, cost[&(u, v)])?; } else if cost.contains_key(&(v, u)) { @@ -333,29 +321,26 @@ impl Graph { } impl Graph { - ///This function adds a single directed weighted edge to the graph. + /// 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]; + let idu = self.get_vertex_id(&u)?; + let idv = self.get_vertex_id(&v)?; self.graph[idu].push(WeightedEdge { w, dest: idv }); Ok(()) } - ///This function lists the negative cycles it manages to find after path_length - ///iterations of the main loop of the Bellman-Ford algorithm. For the classical - ///algorithm, path_length needs to be equal to the number of vertices. However, - ///for particular graph structures like in our case, the algorithm is still correct - ///when path_length is the length of the longest possible simple path. - ///See the formal description of the algorithm for more details. + /// This function lists the negative cycles it manages to find after path_length + /// iterations of the main loop of the Bellman-Ford algorithm. For the classical + /// algorithm, path_length needs to be equal to the number of vertices. However, + /// for particular graph structures like in our case, the algorithm is still correct + /// when path_length is the length of the longest possible simple path. + /// See the formal description of the algorithm for more details. fn list_negative_cycles(&self, path_length: usize) -> Vec> { let nb_vertices = self.graph.len(); - //We start with every vertex at distance 0 of some imaginary extra -1 vertex. + // 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 + // 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 { @@ -369,29 +354,35 @@ impl Graph { } } - //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. + // 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(). + // 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()) + .map(|cycle| { + cycle + .iter() + .rev() + .map(|id| self.id_to_vertex[*id]) + .collect() + }) .collect(); } } -///This function returns the list of cycles of a directed 1 forest. It does not -///check for the consistency of the input. +/// 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]) -> Vec> { let mut cycles = Vec::>::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 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] { @@ -401,8 +392,8 @@ fn cycles_of_1_forest(forest: &[Option]) -> Vec> { } } 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 + // We discovered an id that we explored at this iteration t. + // It means we are on a cycle let mut cy = vec![id; 1]; let mut id2 = id; while let Some(id_next) = forest[id2] { -- cgit v1.2.3 From 73a4ca8b1515f95bf7860fc292c12db83d3c6228 Mon Sep 17 00:00:00 2001 From: Alex Auvolat Date: Mon, 7 Nov 2022 21:12:11 +0100 Subject: Use bytes as capacity units --- src/rpc/graph_algo.rs | 34 +++++++++++++++++----------------- 1 file changed, 17 insertions(+), 17 deletions(-) (limited to 'src/rpc/graph_algo.rs') diff --git a/src/rpc/graph_algo.rs b/src/rpc/graph_algo.rs index 1e4a819b..f181e2ba 100644 --- a/src/rpc/graph_algo.rs +++ b/src/rpc/graph_algo.rs @@ -23,8 +23,8 @@ pub enum Vertex { /// Edge data structure for the flow algorithm. #[derive(Clone, Copy, Debug)] pub struct FlowEdge { - cap: u32, // flow maximal capacity of the edge - flow: i32, // flow value on the edge + cap: u64, // flow maximal capacity of the edge + flow: i64, // flow value on the edge dest: usize, // destination vertex id rev: usize, // index of the reversed edge (v, self) in the edge list of vertex v } @@ -32,7 +32,7 @@ pub struct FlowEdge { /// Edge data structure for the detection of negative cycles. #[derive(Clone, Copy, Debug)] pub struct WeightedEdge { - w: i32, // weight of the edge + w: i64, // weight of the edge dest: usize, } @@ -51,7 +51,7 @@ pub struct Graph { graph: Vec>, } -pub type CostFunction = HashMap<(Vertex, Vertex), i32>; +pub type CostFunction = HashMap<(Vertex, Vertex), i64>; impl Graph { pub fn new(vertices: &[Vertex]) -> Self { @@ -77,7 +77,7 @@ impl Graph { impl Graph { /// 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> { + pub fn add_edge(&mut self, u: Vertex, v: Vertex, c: u64) -> Result<(), String> { let idu = self.get_vertex_id(&u)?; let idv = self.get_vertex_id(&v)?; if idu == idv { @@ -115,7 +115,7 @@ impl Graph { } /// This function returns the value of the flow incoming to v. - pub fn get_inflow(&self, v: Vertex) -> Result { + pub fn get_inflow(&self, v: Vertex) -> Result { let idv = self.get_vertex_id(&v)?; let mut result = 0; for edge in self.graph[idv].iter() { @@ -125,7 +125,7 @@ impl Graph { } /// This function returns the value of the flow outgoing from v. - pub fn get_outflow(&self, v: Vertex) -> Result { + pub fn get_outflow(&self, v: Vertex) -> Result { let idv = self.get_vertex_id(&v)?; let mut result = 0; for edge in self.graph[idv].iter() { @@ -136,7 +136,7 @@ impl Graph { /// This function computes the flow total value by computing the outgoing flow /// from the source. - pub fn get_flow_value(&mut self) -> Result { + pub fn get_flow_value(&mut self) -> Result { self.get_outflow(Vertex::Source) } @@ -156,7 +156,7 @@ impl Graph { } /// Computes an upper bound of the flow on the graph - pub fn flow_upper_bound(&self) -> Result { + pub fn flow_upper_bound(&self) -> Result { let idsource = self.get_vertex_id(&Vertex::Source)?; let mut flow_upper_bound = 0; for edge in self.graph[idsource].iter() { @@ -193,7 +193,7 @@ impl Graph { // 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 { + if edge.cap as i64 - edge.flow > 0 { fifo.push_back((edge.dest, lvl + 1)); } } @@ -216,10 +216,10 @@ impl Graph { lifo.pop(); while let Some((id, _)) = lifo.pop() { let nbd = next_nbd[id]; - self.graph[id][nbd].flow += f as i32; + self.graph[id][nbd].flow += f as i64; let id_rev = self.graph[id][nbd].dest; let nbd_rev = self.graph[id][nbd].rev; - self.graph[id_rev][nbd_rev].flow -= f as i32; + self.graph[id_rev][nbd_rev].flow -= f as i64; } lifo.push((idsource, flow_upper_bound)); continue; @@ -236,9 +236,9 @@ impl Graph { } // else we can try to send flow from id to its nbd let new_flow = min( - f as i32, - self.graph[id][nbd].cap as i32 - self.graph[id][nbd].flow, - ) as u32; + f as i64, + self.graph[id][nbd].cap as i64 - self.graph[id][nbd].flow, + ) as u64; if new_flow == 0 { next_nbd[id] += 1; continue; @@ -302,7 +302,7 @@ impl Graph { let nb_vertices = self.id_to_vertex.len(); for i in 0..nb_vertices { for edge in self.graph[i].iter() { - if edge.cap as i32 - edge.flow > 0 { + if edge.cap as i64 - edge.flow > 0 { // It is possible to send overflow through this edge let u = self.id_to_vertex[i]; let v = self.id_to_vertex[edge.dest]; @@ -322,7 +322,7 @@ impl Graph { impl Graph { /// 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> { + pub fn add_edge(&mut self, u: Vertex, v: Vertex, w: i64) -> Result<(), String> { let idu = self.get_vertex_id(&u)?; let idv = self.get_vertex_id(&v)?; self.graph[idu].push(WeightedEdge { w, dest: idv }); -- cgit v1.2.3 From cb07e6145cf26a9bbbe44fd06090a099030d0750 Mon Sep 17 00:00:00 2001 From: Jonathan Davies Date: Thu, 5 Jan 2023 11:09:25 +0000 Subject: Changed all instances of assignation to assignment. --- src/rpc/graph_algo.rs | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) (limited to 'src/rpc/graph_algo.rs') diff --git a/src/rpc/graph_algo.rs b/src/rpc/graph_algo.rs index f181e2ba..65450d64 100644 --- a/src/rpc/graph_algo.rs +++ b/src/rpc/graph_algo.rs @@ -1,5 +1,5 @@ //! This module deals with graph algorithms. -//! It is used in layout.rs to build the partition to node assignation. +//! It is used in layout.rs to build the partition to node assignment. use rand::prelude::SliceRandom; use std::cmp::{max, min}; @@ -177,7 +177,7 @@ impl Graph { 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, + // assignment, we shuffle the neighbours of the nodes. Hence, // the vertices do not consider their neighbours in the same order. self.shuffle_edges(); -- cgit v1.2.3 From 0088599f52f38ae9e00fe772a416150813e2470b Mon Sep 17 00:00:00 2001 From: Alex Auvolat Date: Mon, 18 Sep 2023 12:17:07 +0200 Subject: new layout: fix clippy lints --- src/rpc/graph_algo.rs | 8 ++++---- 1 file changed, 4 insertions(+), 4 deletions(-) (limited to 'src/rpc/graph_algo.rs') diff --git a/src/rpc/graph_algo.rs b/src/rpc/graph_algo.rs index 65450d64..0e88efc4 100644 --- a/src/rpc/graph_algo.rs +++ b/src/rpc/graph_algo.rs @@ -189,7 +189,7 @@ impl Graph { let mut fifo = VecDeque::new(); fifo.push_back((idsource, 0)); while let Some((id, lvl)) = fifo.pop_front() { - if level[id] == None { + if level[id].is_none() { // it means id has not yet been reached level[id] = Some(lvl); for edge in self.graph[id].iter() { @@ -199,7 +199,7 @@ impl Graph { } } } - if level[idsink] == None { + if level[idsink].is_none() { // There is no residual flow break; } @@ -383,7 +383,7 @@ fn cycles_of_1_forest(forest: &[Option]) -> Vec> { for t in 0..forest.len() { let mut id = t; // while we are on a valid undiscovered node - while time_of_discovery[id] == None { + while time_of_discovery[id].is_none() { time_of_discovery[id] = Some(t); if let Some(i) = forest[id] { id = i; @@ -391,7 +391,7 @@ fn cycles_of_1_forest(forest: &[Option]) -> Vec> { break; } } - if forest[id] != None && time_of_discovery[id] == Some(t) { + if forest[id].is_some() && time_of_discovery[id] == Some(t) { // We discovered an id that we explored at this iteration t. // It means we are on a cycle let mut cy = vec![id; 1]; -- cgit v1.2.3 From 3ecc17f8c5c822ac5785e8a9fef34caf1a3312a2 Mon Sep 17 00:00:00 2001 From: Alex Auvolat Date: Thu, 21 Sep 2023 11:21:35 +0200 Subject: new layout: use deterministic randomness for reproducible results --- src/rpc/graph_algo.rs | 8 ++++++-- 1 file changed, 6 insertions(+), 2 deletions(-) (limited to 'src/rpc/graph_algo.rs') diff --git a/src/rpc/graph_algo.rs b/src/rpc/graph_algo.rs index 0e88efc4..d8c6c9b9 100644 --- a/src/rpc/graph_algo.rs +++ b/src/rpc/graph_algo.rs @@ -1,7 +1,7 @@ //! This module deals with graph algorithms. //! It is used in layout.rs to build the partition to node assignment. -use rand::prelude::SliceRandom; +use rand::prelude::{SeedableRng, SliceRandom}; use std::cmp::{max, min}; use std::collections::HashMap; use std::collections::VecDeque; @@ -143,7 +143,11 @@ impl Graph { /// 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(); + // We use deterministic randomness so that the layout calculation algorihtm + // will output the same thing every time it is run. This way, the results + // pre-calculated in `garage layout show` will match exactly those used + // in practice with `garage layout apply` + let mut rng = rand::rngs::StdRng::from_seed([0x12u8; 32]); for i in 0..self.graph.len() { self.graph[i].shuffle(&mut rng); // We need to update the ids of the reverse edges. -- cgit v1.2.3