Efficient approximation algorithms for bandwidth consecutive multicolorings of graphs

Let G be a graph in which each vertex v has a positive integer weight b(v) and each edge (v,w) has a nonnegative integer weight b(v,w). A bandwidth consecutive multicoloring, simply called a b-coloring of G, assigns each vertex v a specified number b(v) of consecutive positive integers as colors of...

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Bibliographic Details
Published in:Theoretical computer science Vol. 607; pp. 208 - 220
Main Authors: Obata, Yuji, Nishizeki, Takao
Format: Journal Article
Language:English
Published: Elsevier B.V 23.11.2015
Subjects:
Algorithms
Approximation
Approximation algorithm
Bandwidth
Bandwidth consecutive multicoloring
Coloring
Graph coloring
Graph theory
Graphs
Integers
Mathematical analysis
Bandwidth consecutive multicoloring
Approximation algorithm
Graph coloring
ISSN:0304-3975, 1879-2294
Online Access:Get full text
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Summary:Let G be a graph in which each vertex v has a positive integer weight b(v) and each edge (v,w) has a nonnegative integer weight b(v,w). A bandwidth consecutive multicoloring, simply called a b-coloring of G, assigns each vertex v a specified number b(v) of consecutive positive integers as colors of v so that, for each edge (v,w), all integers assigned to vertex v differ from all integers assigned to vertex w by more than b(v,w). The maximum integer assigned to vertices is called the span of the coloring. The b-coloring problem asks to find a b-coloring of a given graph G with the minimum span. In the paper, we present four efficient approximation algorithms for the problem, which have theoretical performance guarantees for the computation time, the span of a found b-coloring and the approximation ratio. We also obtain several upper bounds on the minimum span, expressed in terms of the maximum b-degrees, one of which is an extension of Brooks' theorem on an ordinary coloring.
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ISSN:0304-3975
1879-2294
DOI:10.1016/j.tcs.2015.07.052