TY - GEN

T1 - Algorithms for bandwidth consecutive multicolorings of graphs

AU - Nishikawa, Kazuhide

AU - Nishizeki, Takao

AU - Zhou, Xiao

N1 - Funding Information:
Work partly supported by MEXT-supported Program for the Strategic Research Foundation at Private Universities. Corresponding author. Tel.: +81 22 795 7166. E-mail addresses: nishikawa@kwansei.ac.jp (K. Nishikawa), nishi@kwansei.ac.jp (T. Nishizeki), zhou@ecei.tohoku.ac.jp (X. Zhou).
Copyright:
Copyright 2012 Elsevier B.V., All rights reserved.

PY - 2012

Y1 - 2012

N2 - 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.

AB - 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.

KW - Acyclic orientation

KW - Algorithm

KW - Approximation

KW - Bandwidth coloring

KW - Channel assignment

KW - FPTAS

KW - Multicoloring

KW - Partial k-tree

KW - Series-parallel graph

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U2 - 10.1007/978-3-642-29700-7_11

DO - 10.1007/978-3-642-29700-7_11

M3 - Conference contribution

AN - SCOPUS:84861209258

SN - 9783642296994

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 117

EP - 128

BT - Frontiers in Algorithmics and Algorithmic Aspects in Information and Management - Joint International Conference, FAW-AAIM 2012, Proceedings

T2 - 6th International Frontiers of Algorithmics Workshop, FAW 2012 and 8th International Conference on Algorithmic Aspects of Information and Management, AAIM 2012

Y2 - 14 May 2012 through 16 May 2012

ER -