Algorithms for bandwidth consecutive multicolorings of graphs

Kazuhide Nishikawa, Takao Nishizeki, Xiao Zhou

Research output: Chapter in Book/Report/Conference proceedingConference contribution

2 Citations (Scopus)

Abstract

Let G be a simple 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 of G assigns each vertex v a specified number b(v) of consecutive positive integers 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 a vertex is called the span of the coloring. In the paper, we first investigate fundamental properties of such a coloring. We then obtain a pseudo polynomial-time exact algorithm and a fully polynomial-time approximation scheme for the problem of finding such a coloring of a given series-parallel graph with the minimum span. We finally extend the results to the case where a given graph G is a partial k-tree, that is, G has a bounded tree-width.

Original languageEnglish
Title of host publicationFrontiers in Algorithmics and Algorithmic Aspects in Information and Management - Joint International Conference, FAW-AAIM 2012, Proceedings
Pages117-128
Number of pages12
DOIs
Publication statusPublished - 2012 May 23
Event6th International Frontiers of Algorithmics Workshop, FAW 2012 and 8th International Conference on Algorithmic Aspects of Information and Management, AAIM 2012 - Beijing, China
Duration: 2012 May 142012 May 16

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume7285 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other6th International Frontiers of Algorithmics Workshop, FAW 2012 and 8th International Conference on Algorithmic Aspects of Information and Management, AAIM 2012
CountryChina
CityBeijing
Period12/5/1412/5/16

Keywords

  • Acyclic orientation
  • Algorithm
  • Approximation
  • Bandwidth coloring
  • Channel assignment
  • FPTAS
  • Multicoloring
  • Partial k-tree
  • Series-parallel graph

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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  • Cite this

    Nishikawa, K., Nishizeki, T., & Zhou, X. (2012). Algorithms for bandwidth consecutive multicolorings of graphs. In Frontiers in Algorithmics and Algorithmic Aspects in Information and Management - Joint International Conference, FAW-AAIM 2012, Proceedings (pp. 117-128). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 7285 LNCS). https://doi.org/10.1007/978-3-642-29700-7_11