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Algorithms for Bandwidth Consecutive Multicolorings of Graphs

(Extended Abstract)

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Part of the Lecture Notes in Computer Science book series (LNTCS,volume 7285)

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.

Keywords

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

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Nishikawa, K., Nishizeki, T., Zhou, X. (2012). Algorithms for Bandwidth Consecutive Multicolorings of Graphs. In: Snoeyink, J., Lu, P., Su, K., Wang, L. (eds) Frontiers in Algorithmics and Algorithmic Aspects in Information and Management. Lecture Notes in Computer Science, vol 7285. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-29700-7_11

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  • DOI: https://doi.org/10.1007/978-3-642-29700-7_11

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-29699-4

  • Online ISBN: 978-3-642-29700-7

  • eBook Packages: Computer ScienceComputer Science (R0)