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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| Vydané v: | Theoretical computer science Ročník 607; s. 208 - 220 |
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| Hlavní autori: | , |
| Médium: | Journal Article |
| Jazyk: | English |
| Vydavateľské údaje: |
Elsevier B.V
23.11.2015
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| Predmet: | |
| ISSN: | 0304-3975, 1879-2294 |
| On-line prístup: | Získať plný text |
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| Shrnutí: | 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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| Bibliografia: | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 23 |
| ISSN: | 0304-3975 1879-2294 |
| DOI: | 10.1016/j.tcs.2015.07.052 |