Introduction toDistributed GraphAlgorithms

JukkaSuomela

graph

nodes

graph

nodes

edges+

graph problems

vertexcover

graph problems

vertexcover

graph problems

vertexcover

graph problems

vertexcover

graph algorithms

input output

graph algorithms

“distributed”vs.

“centralised”

centralisedalgorithm

in

out

G = (V,E)V = {1, 2, …}E = {{1,3}, …}

C = {3, 7, …}

centralisedalgorithm

G = (V,E)V = {1, 2, …}E = {{1,3}, …}

C = {3, 7, …}

all input inone location

all output inone location

centralisedalgorithm

G = (V,E)V = {1, 2, …}E = {{1,3}, …}

C = {3, 7, …}

all input inone location

all output inone location

time unit ≈one step ofcomputation

distributedgraph algorithms

graph = computer networknode = computeredge = communication linktime = communication steps

graph: computer network

node:computer

initial information

t = 0

initial information

t = 0

time step: communication

t = 1

time step: communication

t = 2

all nodes in parallel

t = 2

local outputs

t = 2

“0”

“1”

“0”

nodes that output “1”

vertexcover

distributed algorithm

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map from radius-tneighbourhoods tolocal outputs

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distributed algorithm

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trivial: t ≥ diameterfocus: small t

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distributed algorithm

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our research:local algorithms, t = O(1)

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“what can be“computed locally?”

(Naor & Stockmeyer 1995)

“what can be“computed locally?”

• fast and fault-tolerantdistributed algorithms

• understanding socialnetworks, markets,biological systems, …

local algorithms

(bounded-degree graphs)

• vertex cover: 2-approx.

• edge dominating sets

• almost stable matchings

• linear programming…

local algorithms

matching lower bounds!

e.g.: unique identifiers do nothelp with local approximation

general proof techniques

decision problems…

distributed graphalgorithms

localalgorithms:O(1) time

Thanks!