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Garage v0.9 #473

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lx merged 175 commits from next into main 2023-10-10 13:28:29 +00:00
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doc/optimal_layout_report/optimal_layout.tex
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@ -100,13 +100,12 @@ Again, we will represent an assignment $\alpha$ as a flow in a specific graph $G
Given some candidate size value $s$, we describe the oriented weighted graph $G=(V,E)$ with vertex set $V$ arc set $E$.
The set of vertices $V$ contains the source $\mathbf{s}$, the sink $\mathbf{t}$, vertices
$\mathbf{p, p^+, p^-}$ for every partition $p$, vertices $\mathbf{x}_{p,z}$ for every partition $p$ and zone $z$, and vertices $\mathbf{n}$ for every node $n$.
$\mathbf{p^+, p^-}$ for every partition $p$, vertices $\mathbf{x}_{p,z}$ for every partition $p$ and zone $z$, and vertices $\mathbf{n}$ for every node $n$.
The set of arcs $E$ contains:
\begin{itemize}
\item ($\mathbf{s}$,$\mathbf{p}$, $\rho_\mathbf{N}$) for every partition $p$;
\item ($\mathbf{p}$,$\mathbf{p}^+$, $\rho_\mathbf{Z}$) for every partition $p$;
\item ($\mathbf{p}$,$\mathbf{p}^+$, $\rho_\mathbf{N}-\rho_\mathbf{Z}$) for every partition $p$;
\item ($\mathbf{s}$,$\mathbf{p}^+$, $\rho_\mathbf{Z}$) for every partition $p$;
\item ($\mathbf{s}$,$\mathbf{p}^-$, $\rho_\mathbf{N}-\rho_\mathbf{Z}$) for every partition $p$;
\item ($\mathbf{p}^+$,$\mathbf{x}_{p,z}$, 1) for every partition $p$ and zone $z$;
\item ($\mathbf{p}^-$,$\mathbf{x}_{p,z}$, $\rho_\mathbf{N}-\rho_\mathbf{Z}$) for every partition $p$ and zone $z$;
\item ($\mathbf{x}_{p,z}$,$\mathbf{n}$, 1) for every partition $p$, zone $z$ and node $n\in z$;
@ -119,7 +118,7 @@ In the following complexity calculations, we will use the number of vertices and
An assignment $\alpha$ is realizable with partition size $s$ and the redundancy constraints $(\rho_\mathbf{N},\rho_\mathbf{Z})$ if and only if there exists a maximal flow function $f$ in $G$ with total flow $\rho_\mathbf{N}P$, such that the arcs ($\mathbf{x}_{p,z}$,$\mathbf{n}$, 1) used are exactly those for which $p$ is associated to $n$ in $\alpha$.
\end{proposition}
\begin{proof}
Given such flow $f$, we can reconstruct a candidate $\alpha$. In $f$, the flow passing through every $\mathbf{p}$ is $\rho_\mathbf{N}$, and since the outgoing capacity of every $\mathbf{x}_{p,z}$ is 1, every partition is associated to $\rho_\mathbf{N}$ distinct nodes. The fraction $\rho_\mathbf{Z}$ of the flow passing through every $\mathbf{p^+}$ must be spread over as many distinct zones as every arc outgoing from $\mathbf{p^+}$ has capacity 1. So the reconstructed $\alpha$ verifies the redundancy constraints. For every node $n$, the flow between $\mathbf{n}$ and $\mathbf{t}$ corresponds to the number of partitions associated to $n$. By construction of $f$, this does not exceed $\lfloor c_n/s \rfloor$. We assumed that the partition size is $s$, hence this association does not exceed the storage capacity of the nodes.
Given such flow $f$, we can reconstruct a candidate $\alpha$. In $f$, the flow passing through $\mathbf{p^+}$ and $\mathbf{p^-}$ is $\rho_\mathbf{N}$, and since the outgoing capacity of every $\mathbf{x}_{p,z}$ is 1, every partition is associated to $\rho_\mathbf{N}$ distinct nodes. The fraction $\rho_\mathbf{Z}$ of the flow passing through every $\mathbf{p^+}$ must be spread over as many distinct zones as every arc outgoing from $\mathbf{p^+}$ has capacity 1. So the reconstructed $\alpha$ verifies the redundancy constraints. For every node $n$, the flow between $\mathbf{n}$ and $\mathbf{t}$ corresponds to the number of partitions associated to $n$. By construction of $f$, this does not exceed $\lfloor c_n/s \rfloor$. We assumed that the partition size is $s$, hence this association does not exceed the storage capacity of the nodes.
In the other direction, given an assignment $\alpha$, one can similarly check that the facts that $\alpha$ respects the redundancy constraints, and the storage capacities of the nodes, are necessary condition to construct a maximal flow function $f$.
\end{proof}
@ -272,16 +271,16 @@ The distance $d(f,f')$ is bounded by the maximal number of differences in the as
The detection of negative cycle is done with the Bellman-Ford algorithm, whose complexity should normally be $O(\#E\#V)$. In our case, it amounts to $O(P^2ZN)$. Multiplied by the complexity of the outer loop, it amounts to $O(P^3ZN)$ which is a lot when the number of partitions and nodes starts to be large. To avoid that, we adapt the Bellman-Ford algorithm.
The Bellman-Ford algorithm runs $\#V$ iterations of an outer loop, and an inner loop over $E$. The idea is to compute the shortest paths from a source vertex $v$ to all other vertices. After $k$ iterations of the outer loop, the algorithm has computed all shortest path of length at most $k$. All shortest path have length at most $\#V$, so if there is an update in the last iteration of the loop, it means that there is a negative cycle in the graph. The observation that will enable us to improve the complexity is the following:
The Bellman-Ford algorithm runs $\#V$ iterations of an outer loop, and an inner loop over $E$. The idea is to compute the shortest paths from a source vertex $v$ to all other vertices. After $k$ iterations of the outer loop, the algorithm has computed all shortest path of length at most $k$. All simple paths have length at most $\#V-1$, so if there is an update in the last iteration of the loop, it means that there is a negative cycle in the graph. The observation that will enable us to improve the complexity is the following:
\begin{proposition}
In the graph $G_f$ (and $G$), all simple paths and cycles have a length at most $6N$.
In the graph $G_f$ (and $G$), all simple paths have a length at most $4N$.
\end{proposition}
\begin{proof}
Since $f$ is a maximal flow, there is no outgoing edge from $\mathbf{s}$ in $G_f$. One can thus check than any simple path of length 6 must contain at least to node of type $\mathbf{n}$. Hence on a cycle, at most 6 arcs separate two successive nodes of type $\mathbf{n}$.
Since $f$ is a maximal flow, there is no outgoing edge from $\mathbf{s}$ in $G_f$. One can thus check than any simple path of length 4 must contain at least two node of type $\mathbf{n}$. Hence on a path, at most 4 arcs separate two successive nodes of type $\mathbf{n}$.
\end{proof}
Thus, in the absence of negative cycles, shortest paths in $G_f$ have length at most $6N$. So we can do only $6N$ iterations of the outer loop in Bellman-Ford algorithm. This makes the complexity of the detection of one set of cycle to be $O(N\#E) = O(N^2 P)$.
Thus, in the absence of negative cycles, shortest paths in $G_f$ have length at most $4N$. So we can do only $4N+1$ iterations of the outer loop in Bellman-Ford algorithm. This makes the complexity of the detection of one set of cycle to be $O(N\#E) = O(N^2 P)$.
With this improvement, the complexity of the whole algorithm is, in the worst case, $O(N^2P^2)$. However, since we detect several cycles at once and we start with a flow that might be close to the previous one, the number of iterations of the outer loop might be smaller in practice.

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

759
src/rpc/layout.rs
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@ -1,17 +1,23 @@
use std::cmp::min;
use std::cmp::Ordering;
use std::collections::HashMap;
use std::collections::HashSet;
use hex::ToHex;
use serde::{Deserialize, Serialize};
use garage_util::bipartite::*;
use garage_util::crdt::{AutoCrdt, Crdt, LwwMap};
use garage_util::data::*;
use rand::prelude::SliceRandom;
use crate::graph_algo::*;
use crate::ring::*;
use std::convert::TryInto;
//The Message type will be used to collect information on the algorithm.
type Message = Vec<String>;
/// The layout of the cluster, i.e. the list of roles
/// which are assigned to each cluster node
#[derive(Clone, Debug, Serialize, Deserialize)]
@ -19,12 +25,21 @@ pub struct ClusterLayout {
pub version: u64,
pub replication_factor: usize,
#[serde(default="default_one")]
pub zone_redundancy: usize,
//This attribute is only used to retain the previously computed partition size,
//to know to what extent does it change with the layout update.
#[serde(default="default_zero")]
pub partition_size: u32,
pub roles: LwwMap<Uuid, NodeRoleV>,
/// node_id_vec: a vector of node IDs with a role assigned
/// in the system (this includes gateway nodes).
/// The order here is different than the vec stored by `roles`, because:
/// 1. non-gateway nodes are first so that they have lower numbers
/// 1. non-gateway nodes are first so that they have lower numbers holding
/// in u8 (the number of non-gateway nodes is at most 256).
/// 2. nodes that don't have a role are excluded (but they need to
/// stay in the CRDT as tombstones)
pub node_id_vec: Vec<Uuid>,
@ -38,6 +53,15 @@ pub struct ClusterLayout {
pub staging_hash: Hash,
}
fn default_one() -> usize{
return 1;
}
fn default_zero() -> u32{
return 0;
}
const NB_PARTITIONS : usize = 1usize << PARTITION_BITS;
#[derive(PartialEq, Eq, PartialOrd, Ord, Clone, Debug, Serialize, Deserialize)]
pub struct NodeRoleV(pub Option<NodeRole>);
@ -66,16 +90,31 @@ impl NodeRole {
None => "gateway".to_string(),
}
}
pub fn tags_string(&self) -> String {
let mut tags = String::new();
if self.tags.len() == 0 {
return tags
}
tags.push_str(&self.tags[0].clone());
for t in 1..self.tags.len(){
tags.push_str(",");
tags.push_str(&self.tags[t].clone());
}
return tags;
}
}
impl ClusterLayout {
pub fn new(replication_factor: usize) -> Self {
pub fn new(replication_factor: usize, zone_redundancy: usize) -> Self {
let empty_lwwmap = LwwMap::new();
let empty_lwwmap_hash = blake2sum(&rmp_to_vec_all_named(&empty_lwwmap).unwrap()[..]);
ClusterLayout {
version: 0,
replication_factor,
zone_redundancy,
partition_size: 0,
roles: LwwMap::new(),
node_id_vec: Vec::new(),
ring_assignation_data: Vec::new(),
@ -122,6 +161,44 @@ impl ClusterLayout {
}
}
///Returns the uuids of the non_gateway nodes in self.node_id_vec.
pub fn useful_nodes(&self) -> Vec<Uuid> {
let mut result = Vec::<Uuid>::new();
for uuid in self.node_id_vec.iter() {
match self.node_role(uuid) {
Some(role) if role.capacity != None => result.push(*uuid),
_ => ()
}
}
return result;
}
///Given a node uuids, this function returns the label of its zone
pub fn get_node_zone(&self, uuid : &Uuid) -> Result<String,String> {
match self.node_role(uuid) {
Some(role) => return Ok(role.zone.clone()),
_ => return Err("The Uuid does not correspond to a node present in the cluster.".to_string())
}
}
///Given a node uuids, this function returns its capacity or fails if it does not have any
pub fn get_node_capacity(&self, uuid : &Uuid) -> Result<u32,String> {
match self.node_role(uuid) {
Some(NodeRole{capacity : Some(cap), zone: _, tags: _}) => return Ok(*cap),
_ => return Err("The Uuid does not correspond to a node present in the cluster or this node does not have a positive capacity.".to_string())
}
}
///Returns the sum of capacities of non gateway nodes in the cluster
pub fn get_total_capacity(&self) -> Result<u32,String> {
let mut total_capacity = 0;
for uuid in self.useful_nodes().iter() {
total_capacity += self.get_node_capacity(uuid)?;
}
return Ok(total_capacity);
}
/// Check a cluster layout for internal consistency
/// returns true if consistent, false if error
pub fn check(&self) -> bool {
@ -168,342 +245,412 @@ impl ClusterLayout {
true
}
}
impl ClusterLayout {
/// This function calculates a new partition-to-node assignation.
/// The computed assignation maximizes the capacity of a
/// The computed assignation respects the node replication factor
/// and the zone redundancy parameter It maximizes the capacity of a
/// partition (assuming all partitions have the same size).
/// Among such optimal assignation, it minimizes the distance to
/// the former assignation (if any) to minimize the amount of
/// data to be moved. A heuristic ensures node triplets
/// dispersion (in garage_util::bipartite::optimize_matching()).
pub fn calculate_partition_assignation(&mut self) -> bool {
/// data to be moved.
pub fn calculate_partition_assignation(&mut self, replication:usize, redundancy:usize) -> Result<Message,String> {
//The nodes might have been updated, some might have been deleted.
//So we need to first update the list of nodes and retrieve the
//assignation.
let old_node_assignation = self.update_nodes_and_ring();
let (node_zone, _) = self.get_node_zone_capacity();
//We update the node ids, since the node list might have changed with the staged
//changes in the layout. We retrieve the old_assignation reframed with the new ids
let old_assignation_opt = self.update_node_id_vec()?;
self.replication_factor = replication;
self.zone_redundancy = redundancy;
//We compute the optimal number of partition to assign to
//every node and zone.
if let Some((part_per_nod, part_per_zone)) = self.optimal_proportions() {
//We collect part_per_zone in a vec to not rely on the
//arbitrary order in which elements are iterated in
//Hashmap::iter()
let part_per_zone_vec = part_per_zone
.iter()
.map(|(x, y)| (x.clone(), *y))
.collect::<Vec<(String, usize)>>();
//We create an indexing of the zones
let mut zone_id = HashMap::<String, usize>::new();
for (i, ppz) in part_per_zone_vec.iter().enumerate() {
zone_id.insert(ppz.0.clone(), i);
}
let mut msg = Message::new();
msg.push(format!("Computation of a new cluster layout where partitions are
replicated {} times on at least {} distinct zones.", replication, redundancy));
//We compute a candidate for the new partition to zone
//assignation.
let nb_zones = part_per_zone.len();
let nb_nodes = part_per_nod.len();
let nb_partitions = 1 << PARTITION_BITS;
let left_cap_vec = vec![self.replication_factor as u32; nb_partitions];
let right_cap_vec = part_per_zone_vec.iter().map(|(_, y)| *y as u32).collect();
let mut zone_assignation = dinic_compute_matching(left_cap_vec, right_cap_vec);
//We generate for once numerical ids for the zone, to use them as indices in the
//flow graphs.
let (id_to_zone , zone_to_id) = self.generate_zone_ids()?;
//We create the structure for the partition-to-node assignation.
let mut node_assignation = vec![vec![None; self.replication_factor]; nb_partitions];
//We will decrement part_per_nod to keep track of the number
//of partitions that we still have to associate.
let mut part_per_nod = part_per_nod;
msg.push(format!("The cluster contains {} nodes spread over {} zones.",
self.useful_nodes().len(), id_to_zone.len()));
//We minimize the distance to the former assignation(if any)
//We compute the optimal partition size
let partition_size = self.compute_optimal_partition_size(&zone_to_id)?;
if old_assignation_opt != None {
msg.push(format!("Given the replication and redundancy constraint, the
optimal size of a partition is {}. In the previous layout, it used to
be {}.", partition_size, self.partition_size));
}
else {
msg.push(format!("Given the replication and redundancy constraints, the
optimal size of a partition is {}.", partition_size));
}
self.partition_size = partition_size;
//We get the id of the zones of the former assignation
//(and the id no_zone if there is no node assignated)
let no_zone = part_per_zone_vec.len();
let old_zone_assignation: Vec<Vec<usize>> = old_node_assignation
.iter()
.map(|x| {
x.iter()
.map(|id| match *id {
Some(i) => zone_id[&node_zone[i]],
None => no_zone,
})
.collect()
})
.collect();
//We compute a first flow/assignment that is heuristically close to the previous
//assignment
let mut gflow = self.compute_candidate_assignment( &zone_to_id, &old_assignation_opt)?;
//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
if let Some(assoc) = &old_assignation_opt {
//We minimize the distance to the previous assignment.
self.minimize_rebalance_load(&mut gflow, &zone_to_id, &assoc)?;
}
//We need to assign partitions to nodes in their zone
//We first put the nodes assignation that can stay the same
for i in 0..nb_partitions {
for j in 0..self.replication_factor {
if let Some(Some(former_node)) = old_node_assignation[i].iter().find(|x| {
if let Some(id) = x {
zone_id[&node_zone[*id]] == zone_assignation[i][j]
} else {
false
}
}) {
if part_per_nod[*former_node] > 0 {
node_assignation[i][j] = Some(*former_node);
part_per_nod[*former_node] -= 1;
}
}
}
}
msg.append(&mut self.output_stat(&gflow, &old_assignation_opt, &zone_to_id,&id_to_zone)?);
//We complete the assignation of partitions to nodes
let mut rng = rand::thread_rng();
for i in 0..nb_partitions {
for j in 0..self.replication_factor {
if node_assignation[i][j] == None {
let possible_nodes: Vec<usize> = (0..nb_nodes)
.filter(|id| {
zone_id[&node_zone[*id]] == zone_assignation[i][j]
&& part_per_nod[*id] > 0
})
.collect();
assert!(!possible_nodes.is_empty());
//We randomly pick a node
if let Some(nod) = possible_nodes.choose(&mut rng) {
node_assignation[i][j] = Some(*nod);
part_per_nod[*nod] -= 1;
}
}
}
}
//We write the assignation in the 1D table
self.ring_assignation_data = Vec::<CompactNodeType>::new();
for ass in node_assignation {
for nod in ass {
if let Some(id) = nod {
self.ring_assignation_data.push(id as CompactNodeType);
} else {
panic!()
}
}
}
true
} else {
false
}
}
//We update the layout structure
self.update_ring_from_flow(id_to_zone.len() , &gflow)?;
return Ok(msg);
}
/// The LwwMap of node roles might have changed. This function updates the node_id_vec
/// and returns the assignation given by ring, with the new indices of the nodes, and
/// None of the node is not present anymore.
/// None if the node is not present anymore.
/// We work with the assumption that only this function and calculate_new_assignation
/// do modify assignation_ring and node_id_vec.
fn update_nodes_and_ring(&mut self) -> Vec<Vec<Option<usize>>> {
fn update_node_id_vec(&mut self) -> Result< Option< Vec<Vec<usize> > > ,String> {
// (1) We compute the new node list
//Non gateway nodes should be coded on 8bits, hence they must be first in the list
//We build the new node ids
let mut new_non_gateway_nodes: Vec<Uuid> = self.roles.items().iter()
.filter(|(_, _, v)|
match &v.0 {Some(r) if r.capacity != None => true, _=> false })
.map(|(k, _, _)| *k).collect();
if new_non_gateway_nodes.len() > MAX_NODE_NUMBER {
return Err(format!("There are more than {} non-gateway nodes in the new layout. This is not allowed.", MAX_NODE_NUMBER).to_string());
}
let mut new_gateway_nodes: Vec<Uuid> = self.roles.items().iter()
.filter(|(_, _, v)|
match v {NodeRoleV(Some(r)) if r.capacity == None => true, _=> false })
.map(|(k, _, _)| *k).collect();
let nb_useful_nodes = new_non_gateway_nodes.len();
let mut new_node_id_vec = Vec::<Uuid>::new();
new_node_id_vec.append(&mut new_non_gateway_nodes);
new_node_id_vec.append(&mut new_gateway_nodes);
// (2) We retrieve the old association
//We rewrite the old association with the new indices. We only consider partition
//to node assignations where the node is still in use.
let nb_partitions = 1usize << PARTITION_BITS;
let mut old_assignation = vec![ Vec::<usize>::new() ; nb_partitions];
if self.ring_assignation_data.len() == 0 {
//This is a new association
return Ok(None);
}
if self.ring_assignation_data.len() != nb_partitions * self.replication_factor {
return Err("The old assignation does not have a size corresponding to the old replication factor or the number of partitions.".to_string());
}
//We build a translation table between the uuid and new ids
let mut uuid_to_new_id = HashMap::<Uuid, usize>::new();
//We add the indices of only the new non-gateway nodes that can be used in the
//association ring
for i in 0..nb_useful_nodes {
uuid_to_new_id.insert(new_node_id_vec[i], i );
}
let rf= self.replication_factor;
for p in 0..nb_partitions {
for old_id in &self.ring_assignation_data[p*rf..(p+1)*rf] {
let uuid = self.node_id_vec[*old_id as usize];
if uuid_to_new_id.contains_key(&uuid) {
old_assignation[p].push(uuid_to_new_id[&uuid]);
}
}
}
//We write the results
self.node_id_vec = new_node_id_vec;
self.ring_assignation_data = Vec::<CompactNodeType>::new();
return Ok(Some(old_assignation));
}
///This function generates ids for the zone of the nodes appearing in
///self.node_id_vec.
fn generate_zone_ids(&self) -> Result<(Vec<String>, HashMap<String, usize>),String>{
let mut id_to_zone = Vec::<String>::new();
let mut zone_to_id = HashMap::<String,usize>::new();
for uuid in self.node_id_vec.iter() {
if self.roles.get(uuid) == None {
return Err("The uuid was not found in the node roles (this should not happen, it might be a critical error).".to_string());
}
match self.node_role(&uuid) {
Some(r) => if !zone_to_id.contains_key(&r.zone) && r.capacity != None {
zone_to_id.insert(r.zone.clone() , id_to_zone.len());
id_to_zone.push(r.zone.clone());
}
_ => ()
}
}
return Ok((id_to_zone, zone_to_id));
}
///This function computes by dichotomy the largest realizable partition size, given
///the layout.
fn compute_optimal_partition_size(&self, zone_to_id: &HashMap<String, usize>) -> Result<u32,String>{
let nb_partitions = 1usize << PARTITION_BITS;
let empty_set = HashSet::<(usize,usize)>::new();
let mut g = self.generate_flow_graph(1, zone_to_id, &empty_set)?;
g.compute_maximal_flow()?;
if g.get_flow_value()? < (nb_partitions*self.replication_factor).try_into().unwrap() {
return Err("The storage capacity of he cluster is to small. It is impossible to store partitions of size 1.".to_string());
}
let mut s_down = 1;
let mut s_up = self.get_total_capacity()?;
while s_down +1 < s_up {
g = self.generate_flow_graph((s_down+s_up)/2, zone_to_id, &empty_set)?;
g.compute_maximal_flow()?;
if g.get_flow_value()? < (nb_partitions*self.replication_factor).try_into().unwrap() {
s_up = (s_down+s_up)/2;
}
else {
s_down = (s_down+s_up)/2;
}
}
return Ok(s_down);
}
fn generate_graph_vertices(nb_zones : usize, nb_nodes : usize) -> Vec<Vertex> {
let mut vertices = vec![Vertex::Source, Vertex::Sink];
for p in 0..NB_PARTITIONS {
vertices.push(Vertex::Pup(p));
vertices.push(Vertex::Pdown(p));
for z in 0..nb_zones {
vertices.push(Vertex::PZ(p, z));
}
}
for n in 0..nb_nodes {
vertices.push(Vertex::N(n));
}
return vertices;
}
fn generate_flow_graph(&self, size: u32, zone_to_id: &HashMap<String, usize>, exclude_assoc : &HashSet<(usize,usize)>) -> Result<Graph<FlowEdge>, String> {
let vertices = ClusterLayout::generate_graph_vertices(zone_to_id.len(),
self.useful_nodes().len());
let mut g= Graph::<FlowEdge>::new(&vertices);
let nb_zones = zone_to_id.len();
for p in 0..NB_PARTITIONS {
g.add_edge(Vertex::Source, Vertex::Pup(p), self.zone_redundancy as u32)?;
g.add_edge(Vertex::Source, Vertex::Pdown(p), (self.replication_factor - self.zone_redundancy) as u32)?;
for z in 0..nb_zones {
g.add_edge(Vertex::Pup(p) , Vertex::PZ(p,z) , 1)?;
g.add_edge(Vertex::Pdown(p) , Vertex::PZ(p,z) ,
self.replication_factor as u32)?;
}
}
for n in 0..self.useful_nodes().len() {
let node_capacity = self.get_node_capacity(&self.node_id_vec[n])?;
let node_zone = zone_to_id[&self.get_node_zone(&self.node_id_vec[n])?];
g.add_edge(Vertex::N(n), Vertex::Sink, node_capacity/size)?;
for p in 0..NB_PARTITIONS {
if !exclude_assoc.contains(&(p,n)) {
g.add_edge(Vertex::PZ(p, node_zone), Vertex::N(n), 1)?;
}
}
}
return Ok(g);
}
fn compute_candidate_assignment(&self, zone_to_id: &HashMap<String, usize>,
old_assoc_opt : &Option<Vec< Vec<usize> >>) -> Result<Graph<FlowEdge>, String > {
//We list the edges that are not used in the old association
let mut exclude_edge = HashSet::<(usize,usize)>::new();
if let Some(old_assoc) = old_assoc_opt {
let nb_nodes = self.useful_nodes().len();
for p in 0..NB_PARTITIONS {
for n in 0..nb_nodes {
exclude_edge.insert((p,n));
}
for n in old_assoc[p].iter() {
exclude_edge.remove(&(p,*n));
}
}
}
//We compute the best flow using only the edges used in the old assoc
let mut g = self.generate_flow_graph(self.partition_size, zone_to_id, &exclude_edge )?;
g.compute_maximal_flow()?;
for (p,n) in exclude_edge.iter() {
let node_zone = zone_to_id[&self.get_node_zone(&self.node_id_vec[*n])?];
g.add_edge(Vertex::PZ(*p,node_zone), Vertex::N(*n), 1)?;
}
g.compute_maximal_flow()?;
return Ok(g);
}
fn minimize_rebalance_load(&self, gflow: &mut Graph<FlowEdge>, zone_to_id: &HashMap<String, usize>, old_assoc : &Vec< Vec<usize> >) -> Result<(), String > {
let mut cost = CostFunction::new();
for p in 0..NB_PARTITIONS {
for n in old_assoc[p].iter() {
let node_zone = zone_to_id[&self.get_node_zone(&self.node_id_vec[*n])?];
cost.insert((Vertex::PZ(p,node_zone), Vertex::N(*n)), -1);
}
}
let nb_nodes = self.useful_nodes().len();
let path_length = 4*nb_nodes;
gflow.optimize_flow_with_cost(&cost, path_length)?;
return Ok(());
}
fn update_ring_from_flow(&mut self, nb_zones : usize, gflow: &Graph<FlowEdge> ) -> Result<(), String>{
self.ring_assignation_data = Vec::<CompactNodeType>::new();
for p in 0..NB_PARTITIONS {
for z in 0..nb_zones {
let assoc_vertex = gflow.get_positive_flow_from(Vertex::PZ(p,z))?;
for vertex in assoc_vertex.iter() {
match vertex{
Vertex::N(n) => self.ring_assignation_data.push((*n).try_into().unwrap()),
_ => ()
}
}
}
}
if self.ring_assignation_data.len() != NB_PARTITIONS*self.replication_factor {
return Err("Critical Error : the association ring we produced does not have the right size.".to_string());
}
return Ok(());
}
//This function returns a message summing up the partition repartition of the new
//layout.
fn output_stat(&self , gflow : &Graph<FlowEdge>,
old_assoc_opt : &Option< Vec<Vec<usize>> >,
zone_to_id: &HashMap<String, usize>,
id_to_zone : &Vec<String>) -> Result<Message, String>{
let mut msg = Message::new();
let nb_partitions = 1usize << PARTITION_BITS;
let mut node_assignation = vec![vec![None; self.replication_factor]; nb_partitions];
let rf = self.replication_factor;
let ring = &self.ring_assignation_data;
let used_cap = self.partition_size * nb_partitions as u32 *
self.replication_factor as u32;
let total_cap = self.get_total_capacity()?;
let percent_cap = 100.0*(used_cap as f32)/(total_cap as f32);
msg.push(format!("Available capacity / Total cluster capacity: {} / {} ({:.1} %)",
used_cap , total_cap , percent_cap ));
msg.push(format!("If the percentage is to low, it might be that the replication/redundancy constraints force the use of nodes/zones with small storage capacities.
You might want to rebalance the storage capacities or relax the constraints. See the detailed statistics below and look for saturated nodes/zones."));
msg.push(format!("Recall that because of the replication, the actual available storage capacity is {} / {} = {}.", used_cap , self.replication_factor , used_cap/self.replication_factor as u32));
let new_node_id_vec: Vec<Uuid> = self.roles.items().iter().map(|(k, _, _)| *k).collect();
//We define and fill in the following tables
let storing_nodes = self.useful_nodes();
let mut new_partitions = vec![0; storing_nodes.len()];
let mut stored_partitions = vec![0; storing_nodes.len()];
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]);
}
}
}
let mut new_partitions_zone = vec![0; id_to_zone.len()];
let mut stored_partitions_zone = vec![0; id_to_zone.len()];
self.node_id_vec = new_node_id_vec;
self.ring_assignation_data = vec![];
node_assignation
}
for p in 0..nb_partitions {
for z in 0..id_to_zone.len() {
let pz_nodes = gflow.get_positive_flow_from(Vertex::PZ(p,z))?;
if pz_nodes.len() > 0 {
stored_partitions_zone[z] += 1;
}
for vert in pz_nodes.iter() {
if let Vertex::N(n) = *vert {
stored_partitions[n] += 1;
if let Some(old_assoc) = old_assoc_opt {
if !old_assoc[p].contains(&n) {
new_partitions[n] += 1;
}
}
}
}
if let Some(old_assoc) = old_assoc_opt {
let mut old_zones_of_p = Vec::<usize>::new();
for n in old_assoc[p].iter() {
old_zones_of_p.push(
zone_to_id[&self.get_node_zone(&self.node_id_vec[*n])?]);
}
if !old_zones_of_p.contains(&z) {
new_partitions_zone[z] += 1;
}
}
}
}
///This function compute the number of partition to assign to
///every node and zone, so that every partition is replicated
///self.replication_factor times and the capacity of a partition
///is maximized.
fn optimal_proportions(&mut self) -> Option<(Vec<usize>, HashMap<String, usize>)> {
let mut zone_capacity: HashMap<String, u32> = HashMap::new();
//We display the statistics
let (node_zone, node_capacity) = self.get_node_zone_capacity();
let nb_nodes = self.node_id_vec.len();
if *old_assoc_opt != None {
let total_new_partitions : usize = new_partitions.iter().sum();
msg.push(format!("A total of {} new copies of partitions need to be \
transferred.", total_new_partitions));
}
msg.push(format!(""));
msg.push(format!("Detailed statistics by zones and nodes."));
for i in 0..nb_nodes {
if zone_capacity.contains_key(&node_zone[i]) {
zone_capacity.insert(
node_zone[i].clone(),
zone_capacity[&node_zone[i]] + node_capacity[i],
);
} else {
zone_capacity.insert(node_zone[i].clone(), node_capacity[i]);
}
}
for z in 0..id_to_zone.len(){
let mut nodes_of_z = Vec::<usize>::new();
for n in 0..storing_nodes.len(){
if self.get_node_zone(&self.node_id_vec[n])? == id_to_zone[z] {
nodes_of_z.push(n);
}
}
let replicated_partitions : usize = nodes_of_z.iter()
.map(|n| stored_partitions[*n]).sum();
msg.push(format!(""));
//Compute the optimal number of partitions per zone
let sum_capacities: u32 = zone_capacity.values().sum();
if *old_assoc_opt != None {
msg.push(format!("Zone {}: {} distinct partitions stored ({} new, \
{} partition copies) ", id_to_zone[z], stored_partitions_zone[z],
new_partitions_zone[z], replicated_partitions));
}
else{
msg.push(format!("Zone {}: {} distinct partitions stored ({} partition \
copies) ",
id_to_zone[z], stored_partitions_zone[z], replicated_partitions));
}
if sum_capacities == 0 {
println!("No storage capacity in the network.");
return None;
}
let available_cap_z : u32 = self.partition_size*replicated_partitions as u32;
let mut total_cap_z = 0;
for n in nodes_of_z.iter() {
total_cap_z += self.get_node_capacity(&self.node_id_vec[*n])?;
}
let percent_cap_z = 100.0*(available_cap_z as f32)/(total_cap_z as f32);
msg.push(format!(" Available capacity / Total capacity: {}/{} ({:.1}%).",
available_cap_z, total_cap_z, percent_cap_z));
msg.push(format!(""));
let nb_partitions = 1 << PARTITION_BITS;
for n in nodes_of_z.iter() {
let available_cap_n = stored_partitions[*n] as u32 *self.partition_size;
let total_cap_n =self.get_node_capacity(&self.node_id_vec[*n])?;
let tags_n = (self.node_role(&self.node_id_vec[*n])
.ok_or("Node not found."))?.tags_string();
msg.push(format!(" Node {}: {} partitions ({} new) ; \
available/total capacity: {} / {} ({:.1}%) ; tags:{}",
&self.node_id_vec[*n].to_vec().encode_hex::<String>(),
stored_partitions[*n],
new_partitions[*n], available_cap_n, total_cap_n,
(available_cap_n as f32)/(total_cap_n as f32)*100.0 ,
tags_n));
}
}
//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();
return Ok(msg);
}
//The replication_factor-1 upper bounds the number of
//part_per_zones that are greater than nb_partitions
for _ in 1..self.replication_factor {
//The number of partitions that are not assignated to
//a zone that takes nb_partitions.
let sum_capleft: u32 = zone_capacity
.keys()
.filter(|k| part_per_zone[*k] < nb_partitions)
.map(|k| zone_capacity[k])
.sum();
//The number of replication of the data that we need
//to ensure.
let repl_left = self.replication_factor
- part_per_zone
.values()
.filter(|x| **x == nb_partitions)
.count();
if repl_left == 0 {
break;
}
for k in zone_capacity.keys() {
if part_per_zone[k] != nb_partitions {
part_per_zone.insert(
k.to_string(),
min(
nb_partitions,
(nb_partitions * zone_capacity[k] as usize * repl_left)
/ sum_capleft as usize,
),
);
}
}
}
//Now we divide the zone's partition share proportionally
//between their nodes.
let mut part_per_nod: Vec<usize> = (0..nb_nodes)
.map(|i| {
(part_per_zone[&node_zone[i]] * node_capacity[i] as usize)
/ zone_capacity[&node_zone[i]] as usize
})
.collect();
//We must update the part_per_zone to make it correspond to
//part_per_nod (because of integer rounding)
part_per_zone = part_per_zone.iter().map(|(k, _)| (k.clone(), 0)).collect();
for i in 0..nb_nodes {
part_per_zone.insert(
node_zone[i].clone(),
part_per_zone[&node_zone[i]] + part_per_nod[i],
);
}
//Because of integer rounding, the total sum of part_per_nod
//might not be replication_factor*nb_partitions.
// We need at most to add 1 to every non maximal value of
// part_per_nod. The capacity of a partition will be bounded
// by the minimal value of
// node_capacity_vec[i]/part_per_nod[i]
// so we try to maximize this minimal value, keeping the
// part_per_zone capped
let discrepancy: usize =
nb_partitions * self.replication_factor - part_per_nod.iter().sum::<usize>();
//We use a stupid O(N^2) algorithm. If the number of nodes
//is actually expected to be high, one should optimize this.
for _ in 0..discrepancy {
if let Some(idmax) = (0..nb_nodes)
.filter(|i| part_per_zone[&node_zone[*i]] < nb_partitions)
.max_by(|i, j| {
(node_capacity[*i] * (part_per_nod[*j] + 1) as u32)
.cmp(&(node_capacity[*j] * (part_per_nod[*i] + 1) as u32))
}) {
part_per_nod[idmax] += 1;
part_per_zone.insert(
node_zone[idmax].clone(),
part_per_zone[&node_zone[idmax]] + 1,
);
}
}
//We check the algorithm consistency
let discrepancy: usize =
nb_partitions * self.replication_factor - part_per_nod.iter().sum::<usize>();
assert!(discrepancy == 0);
assert!(if let Some(v) = part_per_zone.values().max() {
*v <= nb_partitions
} else {
false
});
Some((part_per_nod, part_per_zone))
}
//Returns vectors of zone and capacity; indexed by the same (temporary)
//indices as node_id_vec.
fn get_node_zone_capacity(&self) -> (Vec<String>, Vec<u32>) {
let node_zone = self
.node_id_vec
.iter()
.map(|id_nod| match self.node_role(id_nod) {
Some(NodeRole {
zone,
capacity: _,
tags: _,
}) => zone.clone(),
_ => "".to_string(),
})
.collect();
let node_capacity = self
.node_id_vec
.iter()
.map(|id_nod| match self.node_role(id_nod) {
Some(NodeRole {
zone: _,
capacity: Some(c),
tags: _,
}) => *c,
_ => 0,
})
.collect();
(node_zone, node_capacity)
}
}
//====================================================================================
#[cfg(test)]
mod tests {
use super::*;

2
src/rpc/lib.rs
View file

@ -8,9 +8,11 @@ mod consul;
mod kubernetes;
pub mod layout;
pub mod graph_algo;
pub mod ring;
pub mod system;
mod metrics;
pub mod rpc_helper;

1
src/rpc/ring.rs
View file

@ -40,6 +40,7 @@ pub struct Ring {
// Type to store compactly the id of a node in the system
// Change this to u16 the day we want to have more than 256 nodes in a cluster
pub type CompactNodeType = u8;
pub const MAX_NODE_NUMBER: usize = 256;
// The maximum number of times an object might get replicated
// This must be at least 3 because Garage supports 3-way replication

5
src/rpc/system.rs
View file

@ -97,6 +97,7 @@ pub struct System {
kubernetes_discovery: Option<KubernetesDiscoveryParam>,
replication_factor: usize,
zone_redundancy: usize,
/// The ring
pub ring: watch::Receiver<Arc<Ring>>,
@ -192,6 +193,7 @@ impl System {
network_key: NetworkKey,
background: Arc<BackgroundRunner>,
replication_factor: usize,
zone_redundancy: usize,
config: &Config,
) -> Arc<Self> {
let node_key =
@ -211,7 +213,7 @@ impl System {
"No valid previous cluster layout stored ({}), starting fresh.",
e
);
ClusterLayout::new(replication_factor)
ClusterLayout::new(replication_factor, zone_redundancy)
}
};
@ -285,6 +287,7 @@ impl System {
rpc: RpcHelper::new(netapp.id.into(), fullmesh, background.clone(), ring.clone()),
system_endpoint,
replication_factor,
zone_redundancy,
rpc_listen_addr: config.rpc_bind_addr,
rpc_public_addr,
bootstrap_peers: config.bootstrap_peers.clone(),

363
src/util/bipartite.rs
View file

@ -1,363 +0,0 @@
/*
* This module deals with graph algorithm in complete bipartite
* graphs. 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;
//Graph data structure for the flow algorithm.
#[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,
}
/* 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<usize>],
new_match: &[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];
//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
while 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;
}
}
//The optimal matching is build from the graph structure.
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
}
//This function finds a positive cycle in a bipartite wieghted graph.
fn positive_cycle(
edge_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];
//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, e) in edge_vec.iter().enumerate() {
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![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
}
// 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,
};
// 0 will be the source
graph.push(vec![ed; left_cap_vec.len()]);
for (i, c) in left_cap_vec.iter().enumerate() {
graph[0][i].c = *c 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, c) in right_cap_vec.iter().enumerate() {
graph[1][i].c = *c 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() {
*x as i32
} else {
panic!();
};
lifo.push_back((0, flow_upper_bound));
while 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));
}
}
//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::<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..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];
//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 ?
}

1
src/util/lib.rs
View file

@ -4,7 +4,6 @@
extern crate tracing;
pub mod background;
pub mod bipartite;
pub mod config;
pub mod crdt;
pub mod data;