Randomized Distributed Edge Coloring via an Extension of the Chernoff--Hoeffding Bounds

Certain types of routing, scheduling, and resource-allocation problems in a distributed setting can be modeled as edge-coloring problems. We present fast and simple randomized algorithms for edge coloring a graph in the synchronous distributed point-to-point model of computation. Our algorithms comp...

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Vydané v:SIAM journal on computing Ročník 26; číslo 2; s. 350 - 368
Hlavní autori: Panconesi, Alessandro, Srinivasan, Aravind
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Philadelphia, PA Society for Industrial and Applied Mathematics 01.03.1997
Predmet:
Algorithmics. Computability. Computer arithmetics
Algorithms
Applied sciences
Codes
Combinatorial probability
Combinatorics
Combinatorics. Ordered structures
Communication
Computer science
Computer science; control theory; systems
Distributed processing
Exact sciences and technology
Graph theory
Information retrieval. Graph
Mathematics
Probability
Probability and statistics
Probability theory and stochastic processes
Random variables
Scholarships & fellowships
Sciences and techniques of general use
Theoretical computing
Edge(graph)
Tail probability
Graph node
Resource allocation
Graph theory
Parallel algorithms
Large deviation
Randomization
Algorithm performance
Correlation analysis
Distributed algorithm
Graph colouring
Fast algorithm
ISSN:0097-5397, 1095-7111
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Shrnutí:Certain types of routing, scheduling, and resource-allocation problems in a distributed setting can be modeled as edge-coloring problems. We present fast and simple randomized algorithms for edge coloring a graph in the synchronous distributed point-to-point model of computation. Our algorithms compute an edge coloring of a graph $G$ with $n$ nodes and maximum degree $\Delta$ with at most $1.6 \Delta + O(\log^{1+ \delta} n)$ colors with high probability (arbitrarily close to 1) for any fixed $\delta > 0$; they run in polylogarithmic time. The upper bound on the number of colors improves upon the $(2 \Delta - 1)$-coloring achievable by a simple reduction to vertex coloring. To analyze the performance of our algorithms, we introduce new techniques for proving upper bounds on the tail probabilities of certain random variables. The Chernoff--Hoeffding bounds are fundamental tools that are used very frequently in estimating tail probabilities. However, they assume stochastic independence among certain random variables, which may not always hold. Our results extend the Chernoff--Hoeffding bounds to certain types of random variables which are not stochastically independent. We believe that these results are of independent interest and merit further study.
Bibliografia:ObjectType-Article-1
SourceType-Scholarly Journals-1
content type line 14
ISSN:0097-5397
1095-7111
DOI:10.1137/S0097539793250767