Bandwidth of convex bipartite graphs and related graphs

Authors:
Anish Man Singh Shrestha;Satoshi Tayu;Shuichi Ueno
Affiliations:
Department of Communications and Integrated Systems, Tokyo Institute of Technology;Department of Communications and Integrated Systems, Tokyo Institute of Technology;Department of Communications and Integrated Systems, Tokyo Institute of Technology
Venue:
COCOON'11 Proceedings of the 17th annual international conference on Computing and combinatorics
Year:
2011

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Abstract

It is known that the bandwidth problem is NP-complete for chordal bipartite graphs, while the problem can be solved in polynomial time for bipartite permutation graphs, which is a subclass of chordal bipartite graphs. This paper shows that the problem is NP-complete even for convex bipartite graphs, a subclass of chordal bipartite graphs and a superclass of bipartite permutation graphs. We provide an O(n)-time, 4-approximation algorithm and an O(n log2 n)-time, 2-approximation algorithm for convex bipartite graphs with n vertices. For 2-directional orthogonal ray graphs, which is a subclass of chordal bipartite graphs and a superclass of convex bipartite graphs, we provide an O(n2 log n)-time, 3-approximation algorithm, where n is the number of vertices.