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Alex 2022-05-01 09:57:05 +02:00
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430
src/rpc/layout.rs
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@ -1,12 +1,12 @@
use std::cmp::min;
use std::cmp::Ordering;
use std::cmp::{min};
use std::collections::{HashMap};
use std::collections::HashMap;
use serde::{Deserialize, Serialize};
use garage_util::bipartite::*;
use garage_util::crdt::{AutoCrdt, Crdt, LwwMap};
use garage_util::data::*;
use garage_util::bipartite::*;
use rand::prelude::SliceRandom;
@ -168,7 +168,6 @@ impl ClusterLayout {
true
}
/// This function calculates a new partition-to-node assignation.
/// The computed assignation maximizes the capacity of a
/// partition (assuming all partitions have the same size).
@ -177,7 +176,6 @@ impl ClusterLayout {
/// data to be moved. A heuristic ensures node triplets
/// dispersion (in garage_util::bipartite::optimize_matching()).
pub fn calculate_partition_assignation(&mut self) -> bool {
//The nodes might have been updated, some might have been deleted.
//So we need to first update the list of nodes and retrieve the
//assignation.
@ -187,16 +185,17 @@ impl ClusterLayout {
//We compute the optimal number of partition to assign to
//every node and zone.
if let Some((part_per_nod, part_per_zone)) = self.optimal_proportions(){
if let Some((part_per_nod, part_per_zone)) = self.optimal_proportions() {
//We collect part_per_zone in a vec to not rely on the
//arbitrary order in which elements are iterated in
//Hashmap::iter()
let part_per_zone_vec = part_per_zone.iter()
.map(|(x,y)| (x.clone(),*y))
.collect::<Vec<(String,usize)>>();
let part_per_zone_vec = part_per_zone
.iter()
.map(|(x, y)| (x.clone(), *y))
.collect::<Vec<(String, usize)>>();
//We create an indexing of the zones
let mut zone_id = HashMap::<String,usize>::new();
for i in 0..part_per_zone_vec.len(){
let mut zone_id = HashMap::<String, usize>::new();
for i in 0..part_per_zone_vec.len() {
zone_id.insert(part_per_zone_vec[i].0.clone(), i);
}
@ -204,17 +203,13 @@ impl ClusterLayout {
//assignation.
let nb_zones = part_per_zone.len();
let nb_nodes = part_per_nod.len();
let nb_partitions = 1<<PARTITION_BITS;
let left_cap_vec = vec![self.replication_factor as u32 ; nb_partitions];
let right_cap_vec = part_per_zone_vec.iter().map(|(_,y)| *y as u32)
.collect();
let mut zone_assignation =
dinic_compute_matching(left_cap_vec, right_cap_vec);
let nb_partitions = 1 << PARTITION_BITS;
let left_cap_vec = vec![self.replication_factor as u32; nb_partitions];
let right_cap_vec = part_per_zone_vec.iter().map(|(_, y)| *y as u32).collect();
let mut zone_assignation = dinic_compute_matching(left_cap_vec, right_cap_vec);
//We create the structure for the partition-to-node assignation.
let mut node_assignation =
vec![vec![None; self.replication_factor ];nb_partitions];
let mut node_assignation = vec![vec![None; self.replication_factor]; nb_partitions];
//We will decrement part_per_nod to keep track of the number
//of partitions that we still have to associate.
let mut part_per_nod = part_per_nod.clone();
@ -224,27 +219,33 @@ impl ClusterLayout {
//We get the id of the zones of the former assignation
//(and the id no_zone if there is no node assignated)
let no_zone = part_per_zone_vec.len();
let old_zone_assignation : Vec<Vec<usize>> =
old_node_assignation.iter().map(|x| x.iter().map(
|id| match *id { Some(i) => zone_id[&node_zone[i]] ,
None => no_zone }
).collect()).collect();
let old_zone_assignation: Vec<Vec<usize>> = old_node_assignation
.iter()
.map(|x| {
x.iter()
.map(|id| match *id {
Some(i) => zone_id[&node_zone[i]],
None => no_zone,
})
.collect()
})
.collect();
//We minimize the distance to the former zone assignation
zone_assignation = optimize_matching(
&old_zone_assignation, &zone_assignation, nb_zones+1); //+1 for no_zone
zone_assignation =
optimize_matching(&old_zone_assignation, &zone_assignation, nb_zones + 1); //+1 for no_zone
//We need to assign partitions to nodes in their zone
//We first put the nodes assignation that can stay the same
for i in 0..nb_partitions{
for i in 0..nb_partitions {
for j in 0..self.replication_factor {
if let Some(Some(former_node)) = old_node_assignation[i].iter().find(
|x| if let Some(id) = x {
if let Some(Some(former_node)) = old_node_assignation[i].iter().find(|x| {
if let Some(id) = x {
zone_id[&node_zone[*id]] == zone_assignation[i][j]
} else {
false
}
else {false}
)
{
}) {
if part_per_nod[*former_node] > 0 {
node_assignation[i][j] = Some(*former_node);
part_per_nod[*former_node] -= 1;
@ -253,19 +254,20 @@ impl ClusterLayout {
}
}
//We complete the assignation of partitions to nodes
let mut rng = rand::thread_rng();
for i in 0..nb_partitions {
for j in 0..self.replication_factor {
if node_assignation[i][j] == None {
let possible_nodes : Vec<usize> = (0..nb_nodes)
.filter(
|id| zone_id[&node_zone[*id]] == zone_assignation[i][j]
&& part_per_nod[*id] > 0).collect();
assert!(possible_nodes.len()>0);
let possible_nodes: Vec<usize> = (0..nb_nodes)
.filter(|id| {
zone_id[&node_zone[*id]] == zone_assignation[i][j]
&& part_per_nod[*id] > 0
})
.collect();
assert!(possible_nodes.len() > 0);
//We randomly pick a node
if let Some(nod) = possible_nodes.choose(&mut rng){
if let Some(nod) = possible_nodes.choose(&mut rng) {
node_assignation[i][j] = Some(*nod);
part_per_nod[*nod] -= 1;
}
@ -275,18 +277,20 @@ impl ClusterLayout {
//We write the assignation in the 1D table
self.ring_assignation_data = Vec::<CompactNodeType>::new();
for i in 0..nb_partitions{
for i in 0..nb_partitions {
for j in 0..self.replication_factor {
if let Some(id) = node_assignation[i][j] {
self.ring_assignation_data.push(id as CompactNodeType);
} else {
assert!(false)
}
else {assert!(false)}
}
}
true
} else {
false
}
else { false }
}
/// The LwwMap of node roles might have changed. This function updates the node_id_vec
@ -295,21 +299,19 @@ impl ClusterLayout {
/// We work with the assumption that only this function and calculate_new_assignation
/// do modify assignation_ring and node_id_vec.
fn update_nodes_and_ring(&mut self) -> Vec<Vec<Option<usize>>> {
let nb_partitions = 1usize<<PARTITION_BITS;
let mut node_assignation =
vec![vec![None; self.replication_factor ];nb_partitions];
let nb_partitions = 1usize << PARTITION_BITS;
let mut node_assignation = vec![vec![None; self.replication_factor]; nb_partitions];
let rf = self.replication_factor;
let ring = &self.ring_assignation_data;
let new_node_id_vec : Vec::<Uuid> = self.roles.items().iter()
.map(|(k, _, _)| *k)
.collect();
let new_node_id_vec: Vec<Uuid> = self.roles.items().iter().map(|(k, _, _)| *k).collect();
if ring.len() == rf*nb_partitions {
if ring.len() == rf * nb_partitions {
for i in 0..nb_partitions {
for j in 0..self.replication_factor {
node_assignation[i][j] = new_node_id_vec.iter()
.position(|id| *id == self.node_id_vec[ring[i*rf + j] as usize]);
node_assignation[i][j] = new_node_id_vec
.iter()
.position(|id| *id == self.node_id_vec[ring[i * rf + j] as usize]);
}
}
}
@ -324,68 +326,83 @@ impl ClusterLayout {
///self.replication_factor times and the capacity of a partition
///is maximized.
fn optimal_proportions(&mut self) -> Option<(Vec<usize>, HashMap<String, usize>)> {
let mut zone_capacity :HashMap<String, u32>= HashMap::new();
let mut zone_capacity: HashMap<String, u32> = HashMap::new();
let (node_zone, node_capacity) = self.get_node_zone_capacity();
let nb_nodes = self.node_id_vec.len();
for i in 0..nb_nodes
{
for i in 0..nb_nodes {
if zone_capacity.contains_key(&node_zone[i]) {
zone_capacity.insert(node_zone[i].clone(), zone_capacity[&node_zone[i]] + node_capacity[i]);
}
else{
zone_capacity.insert(
node_zone[i].clone(),
zone_capacity[&node_zone[i]] + node_capacity[i],
);
} else {
zone_capacity.insert(node_zone[i].clone(), node_capacity[i]);
}
}
//Compute the optimal number of partitions per zone
let sum_capacities: u32 =zone_capacity.values().sum();
let sum_capacities: u32 = zone_capacity.values().sum();
if sum_capacities <= 0 {
println!("No storage capacity in the network.");
return None;
}
let nb_partitions = 1<<PARTITION_BITS;
let nb_partitions = 1 << PARTITION_BITS;
//Initially we would like to use zones porportionally to
//their capacity.
//However, a large zone can be associated to at most
//nb_partitions to ensure replication of the date.
//So we take the min with nb_partitions:
let mut part_per_zone : HashMap<String, usize> =
zone_capacity.iter()
.map(|(k, v)| (k.clone(), min(nb_partitions,
(self.replication_factor*nb_partitions
**v as usize)/sum_capacities as usize) ) ).collect();
let mut part_per_zone: HashMap<String, usize> = zone_capacity
.iter()
.map(|(k, v)| {
(
k.clone(),
min(
nb_partitions,
(self.replication_factor * nb_partitions * *v as usize)
/ sum_capacities as usize,
),
)
})
.collect();
//The replication_factor-1 upper bounds the number of
//part_per_zones that are greater than nb_partitions
for _ in 1..self.replication_factor {
//The number of partitions that are not assignated to
//a zone that takes nb_partitions.
let sum_capleft : u32 = zone_capacity.keys()
.filter(| k | {part_per_zone[*k] < nb_partitions} )
.map(|k| zone_capacity[k]).sum();
let sum_capleft: u32 = zone_capacity
.keys()
.filter(|k| part_per_zone[*k] < nb_partitions)
.map(|k| zone_capacity[k])
.sum();
//The number of replication of the data that we need
//to ensure.
let repl_left = self.replication_factor
- part_per_zone.values()
.filter(|x| {**x == nb_partitions})
- part_per_zone
.values()
.filter(|x| **x == nb_partitions)
.count();
if repl_left == 0 {
break;
}
for k in zone_capacity.keys() {
if part_per_zone[k] != nb_partitions
{
part_per_zone.insert(k.to_string() , min(nb_partitions,
(nb_partitions*zone_capacity[k] as usize
*repl_left)/sum_capleft as usize));
if part_per_zone[k] != nb_partitions {
part_per_zone.insert(
k.to_string(),
min(
nb_partitions,
(nb_partitions * zone_capacity[k] as usize * repl_left)
/ sum_capleft as usize,
),
);
}
}
}
@ -393,20 +410,21 @@ impl ClusterLayout {
//Now we divide the zone's partition share proportionally
//between their nodes.
let mut part_per_nod : Vec<usize> = (0..nb_nodes).map(
|i| (part_per_zone[&node_zone[i]]*node_capacity[i] as usize)/zone_capacity[&node_zone[i]] as usize
)
let mut part_per_nod: Vec<usize> = (0..nb_nodes)
.map(|i| {
(part_per_zone[&node_zone[i]] * node_capacity[i] as usize)
/ zone_capacity[&node_zone[i]] as usize
})
.collect();
//We must update the part_per_zone to make it correspond to
//part_per_nod (because of integer rounding)
part_per_zone = part_per_zone.iter().map(|(k,_)|
(k.clone(), 0))
.collect();
part_per_zone = part_per_zone.iter().map(|(k, _)| (k.clone(), 0)).collect();
for i in 0..nb_nodes {
part_per_zone.insert(
node_zone[i].clone() ,
part_per_zone[&node_zone[i]] + part_per_nod[i]);
node_zone[i].clone(),
part_per_zone[&node_zone[i]] + part_per_nod[i],
);
}
//Because of integer rounding, the total sum of part_per_nod
@ -418,9 +436,8 @@ impl ClusterLayout {
// so we try to maximize this minimal value, keeping the
// part_per_zone capped
let discrepancy : usize =
nb_partitions*self.replication_factor
- part_per_nod.iter().sum::<usize>();
let discrepancy: usize =
nb_partitions * self.replication_factor - part_per_nod.iter().sum::<usize>();
//We use a stupid O(N^2) algorithm. If the number of nodes
//is actually expected to be high, one should optimize this.
@ -428,194 +445,229 @@ impl ClusterLayout {
for _ in 0..discrepancy {
if let Some(idmax) = (0..nb_nodes)
.filter(|i| part_per_zone[&node_zone[*i]] < nb_partitions)
.max_by( |i,j|
(node_capacity[*i]*(part_per_nod[*j]+1) as u32)
.cmp(&(node_capacity[*j]*(part_per_nod[*i]+1) as u32))
)
{
.max_by(|i, j| {
(node_capacity[*i] * (part_per_nod[*j] + 1) as u32)
.cmp(&(node_capacity[*j] * (part_per_nod[*i] + 1) as u32))
}) {
part_per_nod[idmax] += 1;
part_per_zone.insert(node_zone[idmax].clone(),part_per_zone[&node_zone[idmax]]+1);
part_per_zone.insert(
node_zone[idmax].clone(),
part_per_zone[&node_zone[idmax]] + 1,
);
}
}
//We check the algorithm consistency
let discrepancy : usize =
nb_partitions*self.replication_factor
- part_per_nod.iter().sum::<usize>();
let discrepancy: usize =
nb_partitions * self.replication_factor - part_per_nod.iter().sum::<usize>();
assert!(discrepancy == 0);
assert!(if let Some(v) = part_per_zone.values().max()
{*v <= nb_partitions} else {false} );
assert!(if let Some(v) = part_per_zone.values().max() {
*v <= nb_partitions
} else {
false
});
Some((part_per_nod, part_per_zone))
}
//Returns vectors of zone and capacity; indexed by the same (temporary)
//indices as node_id_vec.
fn get_node_zone_capacity(& self) -> (Vec<String> , Vec<u32>) {
fn get_node_zone_capacity(&self) -> (Vec<String>, Vec<u32>) {
let node_zone = self
.node_id_vec
.iter()
.map(|id_nod| match self.node_role(id_nod) {
Some(NodeRole {
zone,
capacity: _,
tags: _,
}) => zone.clone(),
_ => "".to_string(),
})
.collect();
let node_zone = self.node_id_vec.iter().map(
|id_nod| match self.node_role(id_nod) {
Some(NodeRole{zone,capacity:_,tags:_}) => zone.clone() ,
_ => "".to_string()
let node_capacity = self
.node_id_vec
.iter()
.map(|id_nod| match self.node_role(id_nod) {
Some(NodeRole {
zone: _,
capacity,
tags: _,
}) => {
if let Some(c) = capacity {
*c
} else {
0
}
).collect();
let node_capacity = self.node_id_vec.iter().map(
|id_nod| match self.node_role(id_nod) {
Some(NodeRole{zone:_,capacity,tags:_}) =>
if let Some(c)=capacity
{*c}
else {0},
_ => 0
}
).collect();
_ => 0,
})
.collect();
(node_zone,node_capacity)
(node_zone, node_capacity)
}
}
#[cfg(test)]
mod tests {
use super::*;
use itertools::Itertools;
fn check_assignation(cl : &ClusterLayout) {
fn check_assignation(cl: &ClusterLayout) {
//Check that input data has the right format
let nb_partitions = 1usize<<PARTITION_BITS;
assert!([1,2,3].contains(&cl.replication_factor));
assert!(cl.ring_assignation_data.len() == nb_partitions*cl.replication_factor);
let nb_partitions = 1usize << PARTITION_BITS;
assert!([1, 2, 3].contains(&cl.replication_factor));
assert!(cl.ring_assignation_data.len() == nb_partitions * cl.replication_factor);
let (node_zone, node_capacity) = cl.get_node_zone_capacity();
//Check that is is a correct assignation with zone redundancy
let rf = cl.replication_factor;
for i in 0..nb_partitions{
assert!( rf ==
cl.ring_assignation_data[rf*i..rf*(i+1)].iter()
for i in 0..nb_partitions {
assert!(
rf == cl.ring_assignation_data[rf * i..rf * (i + 1)]
.iter()
.map(|nod| node_zone[*nod as usize].clone())
.unique()
.count() );
.count()
);
}
let nb_nodes = cl.node_id_vec.len();
//Check optimality
let node_nb_part =(0..nb_nodes).map(|i| cl.ring_assignation_data
let node_nb_part = (0..nb_nodes)
.map(|i| {
cl.ring_assignation_data
.iter()
.filter(|x| **x==i as u8)
.count())
.collect::<Vec::<_>>();
.filter(|x| **x == i as u8)
.count()
})
.collect::<Vec<_>>();
let zone_vec = node_zone.iter().unique().collect::<Vec::<_>>();
let zone_nb_part = zone_vec.iter().map( |z| cl.ring_assignation_data.iter()
let zone_vec = node_zone.iter().unique().collect::<Vec<_>>();
let zone_nb_part = zone_vec
.iter()
.map(|z| {
cl.ring_assignation_data
.iter()
.filter(|x| node_zone[**x as usize] == **z)
.count()
).collect::<Vec::<_>>();
})
.collect::<Vec<_>>();
//Check optimality of the zone assignation : would it be better for the
//node_capacity/node_partitions ratio to change the assignation of a partition
if let Some(idmin) = (0..nb_nodes).min_by(
|i,j| (node_capacity[*i]*node_nb_part[*j] as u32)
.cmp(&(node_capacity[*j]*node_nb_part[*i] as u32))
){
if let Some(idmin) = (0..nb_nodes).min_by(|i, j| {
(node_capacity[*i] * node_nb_part[*j] as u32)
.cmp(&(node_capacity[*j] * node_nb_part[*i] as u32))
}) {
if let Some(idnew) = (0..nb_nodes)
.filter( |i| if let Some(p) = zone_vec.iter().position(|z| **z==node_zone[*i])
{zone_nb_part[p] < nb_partitions }
else { false })
.max_by(
|i,j| (node_capacity[*i]*(node_nb_part[*j]as u32+1))
.cmp(&(node_capacity[*j]*(node_nb_part[*i] as u32+1)))
){
assert!(node_capacity[idmin]*(node_nb_part[idnew] as u32+1) >=
node_capacity[idnew]*node_nb_part[idmin] as u32);
.filter(|i| {
if let Some(p) = zone_vec.iter().position(|z| **z == node_zone[*i]) {
zone_nb_part[p] < nb_partitions
} else {
false
}
})
.max_by(|i, j| {
(node_capacity[*i] * (node_nb_part[*j] as u32 + 1))
.cmp(&(node_capacity[*j] * (node_nb_part[*i] as u32 + 1)))
}) {
assert!(
node_capacity[idmin] * (node_nb_part[idnew] as u32 + 1)
>= node_capacity[idnew] * node_nb_part[idmin] as u32
);
}
}
//In every zone, check optimality of the nod assignation
for z in zone_vec {
let node_of_z_iter = (0..nb_nodes).filter(|id| node_zone[*id] == *z );
if let Some(idmin) = node_of_z_iter.clone().min_by(
|i,j| (node_capacity[*i]*node_nb_part[*j] as u32)
.cmp(&(node_capacity[*j]*node_nb_part[*i] as u32))
){
if let Some(idnew) = node_of_z_iter.min_by(
|i,j| (node_capacity[*i]*(node_nb_part[*j] as u32+1))
.cmp(&(node_capacity[*j]*(node_nb_part[*i] as u32+1)))
){
assert!(node_capacity[idmin]*(node_nb_part[idnew] as u32+1) >=
node_capacity[idnew]*node_nb_part[idmin] as u32);
let node_of_z_iter = (0..nb_nodes).filter(|id| node_zone[*id] == *z);
if let Some(idmin) = node_of_z_iter.clone().min_by(|i, j| {
(node_capacity[*i] * node_nb_part[*j] as u32)
.cmp(&(node_capacity[*j] * node_nb_part[*i] as u32))
}) {
if let Some(idnew) = node_of_z_iter.min_by(|i, j| {
(node_capacity[*i] * (node_nb_part[*j] as u32 + 1))
.cmp(&(node_capacity[*j] * (node_nb_part[*i] as u32 + 1)))
}) {
assert!(
node_capacity[idmin] * (node_nb_part[idnew] as u32 + 1)
>= node_capacity[idnew] * node_nb_part[idmin] as u32
);
}
}
}
}
}
fn update_layout(cl : &mut ClusterLayout, node_id_vec : &Vec<u8>,
node_capacity_vec : &Vec<u32> , node_zone_vec : &Vec<String>) {
for i in 0..node_id_vec.len(){
if let Some(x) = FixedBytes32::try_from(&[i as u8;32]) {
fn update_layout(
cl: &mut ClusterLayout,
node_id_vec: &Vec<u8>,
node_capacity_vec: &Vec<u32>,
node_zone_vec: &Vec<String>,
) {
for i in 0..node_id_vec.len() {
if let Some(x) = FixedBytes32::try_from(&[i as u8; 32]) {
cl.node_id_vec.push(x);
}
let update = cl.roles.update_mutator(cl.node_id_vec[i] ,
NodeRoleV(Some(NodeRole{
zone : (node_zone_vec[i].to_string()),
capacity : (Some(node_capacity_vec[i])),
tags : (vec![])})));
let update = cl.roles.update_mutator(
cl.node_id_vec[i],
NodeRoleV(Some(NodeRole {
zone: (node_zone_vec[i].to_string()),
capacity: (Some(node_capacity_vec[i])),
tags: (vec![]),
})),
);
cl.roles.merge(&update);
}
}
#[test]
fn test_assignation() {
let mut node_id_vec = vec![1,2,3];
let mut node_capacity_vec = vec![4000,1000,2000];
let mut node_zone_vec= vec!["A", "B", "C"].into_iter().map(|x| x.to_string()).collect();
let mut node_id_vec = vec![1, 2, 3];
let mut node_capacity_vec = vec![4000, 1000, 2000];
let mut node_zone_vec = vec!["A", "B", "C"]
.into_iter()
.map(|x| x.to_string())
.collect();
let mut cl = ClusterLayout {
node_id_vec: vec![],
roles : LwwMap::new(),
roles: LwwMap::new(),
replication_factor: 3,
ring_assignation_data : vec![],
version:0,
ring_assignation_data: vec![],
version: 0,
staging: LwwMap::new(),
staging_hash: sha256sum(&[1;32]),
staging_hash: sha256sum(&[1; 32]),
};
update_layout(&mut cl, &node_id_vec, &node_capacity_vec, &node_zone_vec);
cl.calculate_partition_assignation();
check_assignation(&cl);
node_id_vec = vec![1,2,3, 4, 5, 6, 7, 8, 9];
node_capacity_vec = vec![4000,1000,1000, 3000, 1000, 1000, 2000, 10000, 2000];
node_zone_vec= vec!["A", "B", "C", "C", "C", "B", "G", "H", "I"].into_iter().map(|x| x.to_string()).collect();
node_id_vec = vec![1, 2, 3, 4, 5, 6, 7, 8, 9];
node_capacity_vec = vec![4000, 1000, 1000, 3000, 1000, 1000, 2000, 10000, 2000];
node_zone_vec = vec!["A", "B", "C", "C", "C", "B", "G", "H", "I"]
.into_iter()
.map(|x| x.to_string())
.collect();
update_layout(&mut cl, &node_id_vec, &node_capacity_vec, &node_zone_vec);
cl.calculate_partition_assignation();
check_assignation(&cl);
node_capacity_vec = vec![4000,1000,2000, 7000, 1000, 1000, 2000, 10000, 2000];
node_capacity_vec = vec![4000, 1000, 2000, 7000, 1000, 1000, 2000, 10000, 2000];
update_layout(&mut cl, &node_id_vec, &node_capacity_vec, &node_zone_vec);
cl.calculate_partition_assignation();
check_assignation(&cl);
node_capacity_vec = vec![4000,4000,2000, 7000, 1000, 9000, 2000, 10, 2000];
node_capacity_vec = vec![4000, 4000, 2000, 7000, 1000, 9000, 2000, 10, 2000];
update_layout(&mut cl, &node_id_vec, &node_capacity_vec, &node_zone_vec);
cl.calculate_partition_assignation();
check_assignation(&cl);
}
}

236
src/util/bipartite.rs
View file

@ -4,59 +4,58 @@
* 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
* 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<Vec<usize>> ,
new_match : &Vec<Vec<usize>> ,
nb_right : usize )
-> Vec<Vec<usize>> {
pub fn optimize_matching(
old_match: &Vec<Vec<usize>>,
new_match: &Vec<Vec<usize>>,
nb_right: usize,
) -> Vec<Vec<usize>> {
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];
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 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)) {
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);
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;
}
}
@ -73,47 +72,48 @@ pub fn optimize_matching( old_match : &Vec<Vec<usize>> ,
//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{
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].u, edge_vec[i].v) = (edge_vec[i].v, edge_vec[i].u);
edge_vec[i].w *= -1;
}
}
else {
} 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::<usize>::new() ; nb_left];
let mut matching = vec![Vec::<usize>::new(); nb_left];
for e in edge_vec {
if e.u > e.v {
matching[e.v].push(e.u-nb_left);
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<WeightedEdge>, nb_left : usize,
nb_right : usize) -> Option<Vec<usize>> {
fn positive_cycle(
edge_vec: &Vec<WeightedEdge>,
nb_left: usize,
nb_right: usize,
) -> Option<Vec<usize>> {
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];
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{
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];
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
@ -121,11 +121,11 @@ fn positive_cycle( edge_vec : &Vec<WeightedEdge>, nb_left : usize,
//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 _ 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;
if weight[e.v] < weight[e.u] + e.w {
weight[e.v] = weight[e.u] + e.w;
prev[e.v] = j;
}
}
@ -138,12 +138,12 @@ fn positive_cycle( edge_vec : &Vec<WeightedEdge>, nb_left : usize,
}
//We detect positive cycle
for e in edge_vec {
if weight[e.v] < weight[e.u]+e.w {
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 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]{
while !was_seen[curr] {
was_seen[curr] = true;
curr = edge_vec[prev[curr]].u;
}
@ -164,62 +164,62 @@ fn positive_cycle( edge_vec : &Vec<WeightedEdge>, nb_left : usize,
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<u32>,
right_cap_vec : Vec<u32>) -> Vec< Vec<usize> >
{
let mut graph = Vec::<Vec::<EdgeFlow> >::new();
let ed = EdgeFlow{c:0,flow:0,v:0, rev:0};
pub fn dinic_compute_matching(left_cap_vec: Vec<u32>, right_cap_vec: Vec<u32>) -> Vec<Vec<usize>> {
let mut graph = Vec::<Vec<EdgeFlow>>::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.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].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.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].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;
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;
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;
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;
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;
}
}
@ -240,19 +240,19 @@ pub fn dinic_compute_matching( left_cap_vec : Vec<u32>,
let nb_vertices = graph.len();
//We run Dinic's max flow algorithm
loop{
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));
fifo.push_back((0, 0));
while !fifo.is_empty() {
if let Some((id,lvl)) = fifo.pop_front(){
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));
for e in graph[id].iter() {
if e.c - e.flow > 0 {
fifo.push_back((e.v, lvl + 1));
}
}
}
@ -269,17 +269,15 @@ pub fn dinic_compute_matching( left_cap_vec : Vec<u32>,
let flow_upper_bound;
if let Some(x) = left_cap_vec.iter().max() {
flow_upper_bound=*x as i32;
}
else {
flow_upper_bound = *x as i32;
} else {
flow_upper_bound = 0;
assert!(false);
}
lifo.push_back((0,flow_upper_bound));
lifo.push_back((0, flow_upper_bound));
loop
{
loop {
if let Some((id_tmp, f_tmp)) = lifo.back() {
let id = *id_tmp;
let f = *f_tmp;
@ -288,15 +286,15 @@ pub fn dinic_compute_matching( left_cap_vec : Vec<u32>,
//residual flow.
lifo.pop_back();
while !lifo.is_empty() {
if let Some((id,_)) = lifo.pop_back(){
let nbd=next_nbd[id];
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));
lifo.push_back((0, flow_upper_bound));
continue;
}
//else we did not reach the sink
@ -304,75 +302,75 @@ pub fn dinic_compute_matching( left_cap_vec : Vec<u32>,
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;
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 {
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 {
} else {
break;
}
}
}
//We return the association
let assoc_table = (0..left_cap_vec.len()).map(
|id| graph[id+2].iter()
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();
.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::<i32>() == 0);
for e in graph[i].iter(){
for i in 3..graph.len() {
assert!(graph[i].iter().map(|e| e.flow).sum::<i32>() == 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::<i32>());
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::<i32>());
}
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::<i32>());
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::<i32>()
);
}
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];
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 ?
}