On the Cubicity of AT-Free Graphs and Circular-Arc Graphs
Graph Theory, Computational Intelligence and Thought
Hardness results for approximating the bandwidth
Journal of Computer and System Sciences
Optimal linear arrangement of interval graphs
MFCS'06 Proceedings of the 31st international conference on Mathematical Foundations of Computer Science
Reduced clique graphs of chordal graphs
European Journal of Combinatorics
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We examine the bandwidth problem in circular-arc graphs, chordal graphs with a bounded number of leaves in the clique tree, and k-polygon graphs (fixed k). We show that all of these graph classes admit efficient approximation algorithms which are based on exact or approximate bandwidth layouts of related interval graphs. Specifically, we obtain a bandwidth approximation algorithm for circular-arc graphs that executes in O(n log2 n) time and has performance ratio 2, which is the best possible performance ratio of any polynomial time bandwidth approximation algorithm for circular-arc graphs. For chordal graphs with at most k leaves in the clique tree, we obtain a performance ratio of 2k in O(k(n+m)) time, and our algorithm for k-polygon graphs has performance ratio 2k2 and runs in time O(n3).