From 2aeaddd5e2e1911b084f6d49ccb2236b7fec31af Mon Sep 17 00:00:00 2001 From: Alex Auvolat Date: Sun, 1 May 2022 09:57:05 +0200 Subject: Apply cargo fmt --- src/util/bipartite.rs | 694 +++++++++++++++++++++++++------------------------- 1 file changed, 346 insertions(+), 348 deletions(-) (limited to 'src/util') diff --git a/src/util/bipartite.rs b/src/util/bipartite.rs index aec7b042..ade831a4 100644 --- a/src/util/bipartite.rs +++ b/src/util/bipartite.rs @@ -1,378 +1,376 @@ /* - * This module deals with graph algorithm in complete bipartite + * This module deals with graph algorithm in complete bipartite * graphs. It is used in layout.rs to build the partition to node * assignation. * */ -use std::cmp::{min,max}; -use std::collections::VecDeque; use rand::prelude::SliceRandom; +use std::cmp::{max, min}; +use std::collections::VecDeque; //Graph data structure for the flow algorithm. -#[derive(Clone,Copy,Debug)] -struct EdgeFlow{ - c : i32, - flow : i32, - v : usize, - rev : usize, +#[derive(Clone, Copy, Debug)] +struct EdgeFlow { + c: i32, + flow: i32, + v: usize, + rev: usize, } //Graph data structure for the detection of positive cycles. -#[derive(Clone,Copy,Debug)] -struct WeightedEdge{ - w : i32, - u : usize, - v : usize, +#[derive(Clone, Copy, Debug)] +struct WeightedEdge { + w: i32, + u: usize, + v: usize, } - -/* This function takes two matchings (old_match and new_match) in a - * complete bipartite graph. It returns a matching that has the +/* This function takes two matchings (old_match and new_match) in a + * complete bipartite graph. It returns a matching that has the * same degree as new_match at every vertex, and that is as close * as possible to old_match. * */ -pub fn optimize_matching( old_match : &Vec> , - new_match : &Vec> , - nb_right : usize ) - -> Vec> { - let nb_left = old_match.len(); - let ed = WeightedEdge{w:-1,u:0,v:0}; - let mut edge_vec = vec![ed ; nb_left*nb_right]; - - //We build the complete bipartite graph structure, represented - //by the list of all edges. - for i in 0..nb_left { - for j in 0..nb_right{ - edge_vec[i*nb_right + j].u = i; - edge_vec[i*nb_right + j].v = nb_left+j; - } - } - - for i in 0..edge_vec.len() { - //We add the old matchings - if old_match[edge_vec[i].u].contains(&(edge_vec[i].v-nb_left)) { - edge_vec[i].w *= -1; - } - //We add the new matchings - if new_match[edge_vec[i].u].contains(&(edge_vec[i].v-nb_left)) { - (edge_vec[i].u,edge_vec[i].v) = - (edge_vec[i].v,edge_vec[i].u); - edge_vec[i].w *= -1; - } - } - //Now edge_vec is a graph where edges are oriented LR if we - //can add them to new_match, and RL otherwise. If - //adding/removing them makes the matching closer to old_match - //they have weight 1; and -1 otherwise. - - //We shuffle the edge list so that there is no bias depending in - //partitions/zone label in the triplet dispersion - let mut rng = rand::thread_rng(); - edge_vec.shuffle(&mut rng); - - //Discovering and flipping a cycle with positive weight in this - //graph will make the matching closer to old_match. - //We use Bellman Ford algorithm to discover positive cycles - loop{ - if let Some(cycle) = positive_cycle(&edge_vec, nb_left, nb_right) { - for i in cycle { - //We flip the edges of the cycle. - (edge_vec[i].u,edge_vec[i].v) = - (edge_vec[i].v,edge_vec[i].u); - edge_vec[i].w *= -1; - } - } - else { - //If there is no cycle, we return the optimal matching. - break; - } - } - - //The optimal matching is build from the graph structure. - let mut matching = vec![Vec::::new() ; nb_left]; - for e in edge_vec { - if e.u > e.v { - matching[e.v].push(e.u-nb_left); - } - } - matching +pub fn optimize_matching( + old_match: &Vec>, + new_match: &Vec>, + nb_right: usize, +) -> Vec> { + let nb_left = old_match.len(); + let ed = WeightedEdge { w: -1, u: 0, v: 0 }; + let mut edge_vec = vec![ed; nb_left * nb_right]; + + //We build the complete bipartite graph structure, represented + //by the list of all edges. + for i in 0..nb_left { + for j in 0..nb_right { + edge_vec[i * nb_right + j].u = i; + edge_vec[i * nb_right + j].v = nb_left + j; + } + } + + for i in 0..edge_vec.len() { + //We add the old matchings + if old_match[edge_vec[i].u].contains(&(edge_vec[i].v - nb_left)) { + edge_vec[i].w *= -1; + } + //We add the new matchings + if new_match[edge_vec[i].u].contains(&(edge_vec[i].v - nb_left)) { + (edge_vec[i].u, edge_vec[i].v) = (edge_vec[i].v, edge_vec[i].u); + edge_vec[i].w *= -1; + } + } + //Now edge_vec is a graph where edges are oriented LR if we + //can add them to new_match, and RL otherwise. If + //adding/removing them makes the matching closer to old_match + //they have weight 1; and -1 otherwise. + + //We shuffle the edge list so that there is no bias depending in + //partitions/zone label in the triplet dispersion + let mut rng = rand::thread_rng(); + edge_vec.shuffle(&mut rng); + + //Discovering and flipping a cycle with positive weight in this + //graph will make the matching closer to old_match. + //We use Bellman Ford algorithm to discover positive cycles + loop { + if let Some(cycle) = positive_cycle(&edge_vec, nb_left, nb_right) { + for i in cycle { + //We flip the edges of the cycle. + (edge_vec[i].u, edge_vec[i].v) = (edge_vec[i].v, edge_vec[i].u); + edge_vec[i].w *= -1; + } + } else { + //If there is no cycle, we return the optimal matching. + break; + } + } + + //The optimal matching is build from the graph structure. + let mut matching = vec![Vec::::new(); nb_left]; + for e in edge_vec { + if e.u > e.v { + matching[e.v].push(e.u - nb_left); + } + } + matching } //This function finds a positive cycle in a bipartite wieghted graph. -fn positive_cycle( edge_vec : &Vec, nb_left : usize, - nb_right : usize) -> Option> { - let nb_side_min = min(nb_left, nb_right); - let nb_vertices = nb_left+nb_right; - let weight_lowerbound = -((nb_left +nb_right) as i32) -1; - let mut accessed = vec![false ; nb_left]; - - //We try to find a positive cycle accessible from the left - //vertex i. - for i in 0..nb_left{ - if accessed[i] { - continue; - } - let mut weight =vec![weight_lowerbound ; nb_vertices]; - let mut prev =vec![ edge_vec.len() ; nb_vertices]; - weight[i] = 0; - //We compute largest weighted paths from i. - //Since the graph is bipartite, any simple cycle has length - //at most 2*nb_side_min. In the general Bellman-Ford - //algorithm, the bound here is the number of vertices. Since - //the number of partitions can be much larger than the - //number of nodes, we optimize that. - for _ in 0..(2*nb_side_min) { - for j in 0..edge_vec.len() { - let e = edge_vec[j]; - if weight[e.v] < weight[e.u]+e.w { - weight[e.v] = weight[e.u]+e.w; - prev[e.v] = j; - } - } - } - //We update the accessed table - for i in 0..nb_left { - if weight[i] > weight_lowerbound { - accessed[i] = true; - } - } - //We detect positive cycle - for e in edge_vec { - if weight[e.v] < weight[e.u]+e.w { - //it means e is on a path branching from a positive cycle - let mut was_seen = vec![false ; nb_vertices]; - let mut curr = e.u; - //We track back with prev until we reach the cycle. - while !was_seen[curr]{ - was_seen[curr] = true; - curr = edge_vec[prev[curr]].u; - } - //Now curr is on the cycle. We collect the edges ids. - let mut cycle = Vec::::new(); - cycle.push(prev[curr]); - let mut cycle_vert = edge_vec[prev[curr]].u; - while cycle_vert != curr { - cycle.push(prev[cycle_vert]); - cycle_vert = edge_vec[prev[cycle_vert]].u; - } - - return Some(cycle); - } - } - } - - None -} +fn positive_cycle( + edge_vec: &Vec, + nb_left: usize, + nb_right: usize, +) -> Option> { + let nb_side_min = min(nb_left, nb_right); + let nb_vertices = nb_left + nb_right; + let weight_lowerbound = -((nb_left + nb_right) as i32) - 1; + let mut accessed = vec![false; nb_left]; + //We try to find a positive cycle accessible from the left + //vertex i. + for i in 0..nb_left { + if accessed[i] { + continue; + } + let mut weight = vec![weight_lowerbound; nb_vertices]; + let mut prev = vec![edge_vec.len(); nb_vertices]; + weight[i] = 0; + //We compute largest weighted paths from i. + //Since the graph is bipartite, any simple cycle has length + //at most 2*nb_side_min. In the general Bellman-Ford + //algorithm, the bound here is the number of vertices. Since + //the number of partitions can be much larger than the + //number of nodes, we optimize that. + for _ in 0..(2 * nb_side_min) { + for j in 0..edge_vec.len() { + let e = edge_vec[j]; + if weight[e.v] < weight[e.u] + e.w { + weight[e.v] = weight[e.u] + e.w; + prev[e.v] = j; + } + } + } + //We update the accessed table + for i in 0..nb_left { + if weight[i] > weight_lowerbound { + accessed[i] = true; + } + } + //We detect positive cycle + for e in edge_vec { + if weight[e.v] < weight[e.u] + e.w { + //it means e is on a path branching from a positive cycle + let mut was_seen = vec![false; nb_vertices]; + let mut curr = e.u; + //We track back with prev until we reach the cycle. + while !was_seen[curr] { + was_seen[curr] = true; + curr = edge_vec[prev[curr]].u; + } + //Now curr is on the cycle. We collect the edges ids. + let mut cycle = Vec::::new(); + cycle.push(prev[curr]); + let mut cycle_vert = edge_vec[prev[curr]].u; + while cycle_vert != curr { + cycle.push(prev[cycle_vert]); + cycle_vert = edge_vec[prev[cycle_vert]].u; + } -// This function takes two arrays of capacity and computes the -// maximal matching in the complete bipartite graph such that the + return Some(cycle); + } + } + } + + None +} + +// This function takes two arrays of capacity and computes the +// maximal matching in the complete bipartite graph such that the // left vertex i is matched to left_cap_vec[i] right vertices, and // the right vertex j is matched to right_cap_vec[j] left vertices. // To do so, we use Dinic's maximum flow algorithm. -pub fn dinic_compute_matching( left_cap_vec : Vec, - right_cap_vec : Vec) -> Vec< Vec > -{ - let mut graph = Vec:: >::new(); - let ed = EdgeFlow{c:0,flow:0,v:0, rev:0}; - - // 0 will be the source - graph.push(vec![ed ; left_cap_vec.len()]); - for i in 0..left_cap_vec.len() - { - graph[0][i].c = left_cap_vec[i] as i32; - graph[0][i].v = i+2; - graph[0][i].rev = 0; - } - - //1 will be the sink - graph.push(vec![ed ; right_cap_vec.len()]); - for i in 0..right_cap_vec.len() - { - graph[1][i].c = right_cap_vec[i] as i32; - graph[1][i].v = i+2+left_cap_vec.len(); - graph[1][i].rev = 0; - } - - //we add left vertices - for i in 0..left_cap_vec.len() { - graph.push(vec![ed ; 1+right_cap_vec.len()]); - graph[i+2][0].c = 0; //directed - graph[i+2][0].v = 0; - graph[i+2][0].rev = i; - - for j in 0..right_cap_vec.len() { - graph[i+2][j+1].c = 1; - graph[i+2][j+1].v = 2+left_cap_vec.len()+j; - graph[i+2][j+1].rev = i+1; - } - } - - //we add right vertices - for i in 0..right_cap_vec.len() { - let lft_ln = left_cap_vec.len(); - graph.push(vec![ed ; 1+lft_ln]); - graph[i+lft_ln+2][0].c = graph[1][i].c; - graph[i+lft_ln+2][0].v = 1; - graph[i+lft_ln+2][0].rev = i; - - for j in 0..left_cap_vec.len() { - graph[i+2+lft_ln][j+1].c = 0; //directed - graph[i+2+lft_ln][j+1].v = j+2; - graph[i+2+lft_ln][j+1].rev = i+1; - } - } - - //To ensure the dispersion of the triplets generated by the - //assignation, we shuffle the neighbours of the nodes. Hence, - //left vertices do not consider the right ones in the same order. - let mut rng = rand::thread_rng(); - for i in 0..graph.len() { - graph[i].shuffle(&mut rng); - //We need to update the ids of the reverse edges. - for j in 0..graph[i].len() { - let target_v = graph[i][j].v; - let target_rev = graph[i][j].rev; - graph[target_v][target_rev].rev = j; - } - } - - let nb_vertices = graph.len(); - - //We run Dinic's max flow algorithm - loop{ - //We build the level array from Dinic's algorithm. - let mut level = vec![-1; nb_vertices]; - - let mut fifo = VecDeque::new(); - fifo.push_back((0,0)); - while !fifo.is_empty() { - if let Some((id,lvl)) = fifo.pop_front(){ - if level[id] == -1 { - level[id] = lvl; - for e in graph[id].iter(){ - if e.c-e.flow > 0{ - fifo.push_back((e.v,lvl+1)); - } - } - } - } - } - if level[1] == -1 { - //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(); - - let flow_upper_bound; - if let Some(x) = left_cap_vec.iter().max() { - flow_upper_bound=*x as i32; - } - else { - flow_upper_bound = 0; - assert!(false); - } - - lifo.push_back((0,flow_upper_bound)); - - loop - { - if let Some((id_tmp, f_tmp)) = lifo.back() { - let id = *id_tmp; - let f = *f_tmp; - if id == 1 { - //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]; - graph[id][nbd].flow += f; - let id_v = graph[id][nbd].v; - let nbd_v = graph[id][nbd].rev; - graph[id_v][nbd_v].flow -= f; - } - } - lifo.push_back((0,flow_upper_bound)); - continue; - } - //else we did not reach the sink - let nbd = next_nbd[id]; - if nbd >= 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,graph[id][nbd].c - - graph[id][nbd].flow); - if level[graph[id][nbd].v] <= level[id] || - new_flow == 0 { - //We cannot send flow to nbd. - next_nbd[id] += 1; - continue; - } - //otherwise, we send flow to nbd. - lifo.push_back((graph[id][nbd].v, new_flow)); - } - else { - break; - } - } - } - - //We return the association - let assoc_table = (0..left_cap_vec.len()).map( - |id| graph[id+2].iter() - .filter(|e| e.flow > 0) - .map( |e| e.v-2-left_cap_vec.len()) - .collect()).collect(); - - //consistency check - - //it is a flow - for i in 3..graph.len(){ - assert!( graph[i].iter().map(|e| e.flow).sum::() == 0); - for e in graph[i].iter(){ - assert!(e.flow + graph[e.v][e.rev].flow == 0); - } - } - - //it solves the matching problem - for i in 0..left_cap_vec.len(){ - assert!(left_cap_vec[i] as i32 == - graph[i+2].iter().map(|e| max(0,e.flow)).sum::()); - } - for i in 0..right_cap_vec.len(){ - assert!(right_cap_vec[i] as i32 == - graph[i+2+left_cap_vec.len()].iter() - .map(|e| max(0,e.flow)).sum::()); - } - - - assoc_table -} +pub fn dinic_compute_matching(left_cap_vec: Vec, right_cap_vec: Vec) -> Vec> { + let mut graph = Vec::>::new(); + let ed = EdgeFlow { + c: 0, + flow: 0, + v: 0, + rev: 0, + }; + + // 0 will be the source + graph.push(vec![ed; left_cap_vec.len()]); + for i in 0..left_cap_vec.len() { + graph[0][i].c = left_cap_vec[i] as i32; + graph[0][i].v = i + 2; + graph[0][i].rev = 0; + } + + //1 will be the sink + graph.push(vec![ed; right_cap_vec.len()]); + for i in 0..right_cap_vec.len() { + graph[1][i].c = right_cap_vec[i] as i32; + graph[1][i].v = i + 2 + left_cap_vec.len(); + graph[1][i].rev = 0; + } + + //we add left vertices + for i in 0..left_cap_vec.len() { + graph.push(vec![ed; 1 + right_cap_vec.len()]); + graph[i + 2][0].c = 0; //directed + graph[i + 2][0].v = 0; + graph[i + 2][0].rev = i; + + for j in 0..right_cap_vec.len() { + graph[i + 2][j + 1].c = 1; + graph[i + 2][j + 1].v = 2 + left_cap_vec.len() + j; + graph[i + 2][j + 1].rev = i + 1; + } + } + //we add right vertices + for i in 0..right_cap_vec.len() { + let lft_ln = left_cap_vec.len(); + graph.push(vec![ed; 1 + lft_ln]); + graph[i + lft_ln + 2][0].c = graph[1][i].c; + graph[i + lft_ln + 2][0].v = 1; + graph[i + lft_ln + 2][0].rev = i; + + for j in 0..left_cap_vec.len() { + graph[i + 2 + lft_ln][j + 1].c = 0; //directed + graph[i + 2 + lft_ln][j + 1].v = j + 2; + graph[i + 2 + lft_ln][j + 1].rev = i + 1; + } + } + + //To ensure the dispersion of the triplets generated by the + //assignation, we shuffle the neighbours of the nodes. Hence, + //left vertices do not consider the right ones in the same order. + let mut rng = rand::thread_rng(); + for i in 0..graph.len() { + graph[i].shuffle(&mut rng); + //We need to update the ids of the reverse edges. + for j in 0..graph[i].len() { + let target_v = graph[i][j].v; + let target_rev = graph[i][j].rev; + graph[target_v][target_rev].rev = j; + } + } + + let nb_vertices = graph.len(); + + //We run Dinic's max flow algorithm + loop { + //We build the level array from Dinic's algorithm. + let mut level = vec![-1; nb_vertices]; + + let mut fifo = VecDeque::new(); + fifo.push_back((0, 0)); + while !fifo.is_empty() { + if let Some((id, lvl)) = fifo.pop_front() { + if level[id] == -1 { + level[id] = lvl; + for e in graph[id].iter() { + if e.c - e.flow > 0 { + fifo.push_back((e.v, lvl + 1)); + } + } + } + } + } + if level[1] == -1 { + //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(); + + let flow_upper_bound; + if let Some(x) = left_cap_vec.iter().max() { + flow_upper_bound = *x as i32; + } else { + flow_upper_bound = 0; + assert!(false); + } + + lifo.push_back((0, flow_upper_bound)); + + loop { + if let Some((id_tmp, f_tmp)) = lifo.back() { + let id = *id_tmp; + let f = *f_tmp; + if id == 1 { + //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]; + graph[id][nbd].flow += f; + let id_v = graph[id][nbd].v; + let nbd_v = graph[id][nbd].rev; + graph[id_v][nbd_v].flow -= f; + } + } + lifo.push_back((0, flow_upper_bound)); + continue; + } + //else we did not reach the sink + let nbd = next_nbd[id]; + if nbd >= 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, graph[id][nbd].c - graph[id][nbd].flow); + if level[graph[id][nbd].v] <= level[id] || new_flow == 0 { + //We cannot send flow to nbd. + next_nbd[id] += 1; + continue; + } + //otherwise, we send flow to nbd. + lifo.push_back((graph[id][nbd].v, new_flow)); + } else { + break; + } + } + } + + //We return the association + let assoc_table = (0..left_cap_vec.len()) + .map(|id| { + graph[id + 2] + .iter() + .filter(|e| e.flow > 0) + .map(|e| e.v - 2 - left_cap_vec.len()) + .collect() + }) + .collect(); + + //consistency check + + //it is a flow + for i in 3..graph.len() { + assert!(graph[i].iter().map(|e| e.flow).sum::() == 0); + for e in graph[i].iter() { + assert!(e.flow + graph[e.v][e.rev].flow == 0); + } + } + + //it solves the matching problem + for i in 0..left_cap_vec.len() { + assert!(left_cap_vec[i] as i32 == graph[i + 2].iter().map(|e| max(0, e.flow)).sum::()); + } + for i in 0..right_cap_vec.len() { + assert!( + right_cap_vec[i] as i32 + == graph[i + 2 + left_cap_vec.len()] + .iter() + .map(|e| max(0, e.flow)) + .sum::() + ); + } + + assoc_table +} #[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 - let _ = dinic_compute_matching(left_vec, right_vec); - } - - //maybe add tests relative to the matching optilization ? -} + 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 + let _ = dinic_compute_matching(left_vec, right_vec); + } + //maybe add tests relative to the matching optilization ? +} -- cgit v1.2.3