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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Bibliographic Details
Published in:SIAM journal on computing Vol. 21; no. 1; pp. 193 - 201
Main Author: Linial, Nathan
Format: Journal Article
Language:English
Published: Philadelphia, PA Society for Industrial and Applied Mathematics 01.02.1992
Subjects:
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
Online Access:Get full text
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Summary: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 $O(\log ^ * n)$.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
content type line 14
ISSN:0097-5397
1095-7111
DOI:10.1137/0221015