Locality in Distributed Graph Algorithms

This paper concerns a number of algorithmic problems on graphs and how they may be solved in a distributed fashion. The computational model is such that each node of the graph is occupied by a processor which has its own ID. Processors are restricted to collecting data from others which are at a dis...

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Vydáno v:	SIAM journal on computing Ročník 21; číslo 1; s. 193 - 201
Hlavní autor:	Linial, Nathan
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Philadelphia, PA Society for Industrial and Applied Mathematics 01.02.1992
Témata:	Algorithms Combinatorics Combinatorics. Ordered structures Computer science Distributed processing Exact sciences and technology Graph theory Graphs Labeling Mathematics Sciences and techniques of general use Algorithmics Lower bound Distributed processing Graph colouring Algorithm complexity
ISSN:	0097-5397, 1095-7111
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Abstract	This paper concerns a number of algorithmic problems on graphs and how they may be solved in a distributed fashion. The computational model is such that each node of the graph is occupied by a processor which has its own ID. Processors are restricted to collecting data from others which are at a distance at most $t$ away from them in $t$ time units, but are otherwise computationally unbounded. This model focuses on the issue of locality in distributed processing, namely, to what extent a global solution to a computational problem can be obtained from locally available data. Three results are proved within this model: * A 3-coloring of an $n$-cycle requires time $\Omega (\log ^ * n)$. This bound is tight, by previous work of Cole and Vishkin. * Any algorithm for coloring the $d$-regular tree of radius $r$ which runs for time at most $2r/3$ requires at least $\Omega (\sqrt d )$ colors. * In an $n$-vertex graph of largest degree $\Delta $, an $O(\Delta ^2 )$-coloring may be found in time $O(\log ^ * n)$.
AbstractList	This paper concerns a number of algorithmic problems on graphs and how they may be solved in a distributed fashion. The computational model is such that each node of the graph is occupied by a processor which has its own ID. Processors are restricted to collecting data from others which are at a distance at most $t$ away from them in $t$ time units, but are otherwise computationally unbounded. This model focuses on the issue of locality in distributed processing, namely, to what extent a global solution to a computational problem can be obtained from locally available data. Three results are proved within this model: * A 3-coloring of an $n$-cycle requires time $\Omega (\log ^ * n)$. This bound is tight, by previous work of Cole and Vishkin. * Any algorithm for coloring the $d$-regular tree of radius $r$ which runs for time at most $2r/3$ requires at least $\Omega (\sqrt d )$ colors. * In an $n$-vertex graph of largest degree $\Delta $, an $O(\Delta ^2 )$-coloring may be found in time $O(\log ^ * n)$.
Author	Linial, Nathan
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Snippet	This paper concerns a number of algorithmic problems on graphs and how they may be solved in a distributed fashion. The computational model is such that each...
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SubjectTerms	Algorithms Combinatorics Combinatorics. Ordered structures Computer science Distributed processing Exact sciences and technology Graph theory Graphs Labeling Mathematics Sciences and techniques of general use
Title	Locality in Distributed Graph Algorithms
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