Approximating bandwidth by mixing layouts of interval graphs

Abstract

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 eficient 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 not more than 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).