distributed graph algorithms · 2020-05-25 · distributed graph algorithms local algorithms: o(1)...
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Introduction toDistributed GraphAlgorithms
JukkaSuomela
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graph
nodes
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graph
nodes
edges+
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graph problems
vertexcover
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graph problems
vertexcover
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graph problems
vertexcover
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graph problems
vertexcover
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graph algorithms
input output
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graph algorithms
“distributed”vs.
“centralised”
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centralisedalgorithm
in
out
G = (V,E)V = {1, 2, …}E = {{1,3}, …}
C = {3, 7, …}
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centralisedalgorithm
G = (V,E)V = {1, 2, …}E = {{1,3}, …}
C = {3, 7, …}
all input inone location
all output inone location
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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
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distributedgraph algorithms
graph = computer networknode = computeredge = communication linktime = communication steps
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graph: computer network
node:computer
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initial information
t = 0
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initial information
t = 0
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time step: communication
t = 1
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time step: communication
t = 2
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all nodes in parallel
t = 2
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local outputs
t = 2
“0”
“1”
“0”
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nodes that output “1”
vertexcover
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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)
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“what can be“computed locally?”
• fast and fault-tolerantdistributed algorithms
• understanding socialnetworks, markets,biological systems, …
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local algorithms
(bounded-degree graphs)
• vertex cover: 2-approx.
• edge dominating sets
• almost stable matchings
• linear programming…
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local algorithms
matching lower bounds!
e.g.: unique identifiers do nothelp with local approximation
general proof techniques
decision problems…
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distributed graphalgorithms
localalgorithms:O(1) time
Thanks!