Efficient Enumeration of Maximal and Maximum Independent Sets of an Interval Graph and a Circular-Arc Graph.

Abstract

We present efficient algorithms for generating all maximal and all maximum independent sets of an interval graph and a circular- arc graph. When an interval graph is given in the form of a family of n intervals, the first and second algorithms produce all maximal and all maximum independent sets, respectively, in O(n DOT log n+ (the size of an output)) time. When a circular- arc graph is given in the form of a family of n arcs on a circle, the third algorithm generates all maximal independent sets in O(n log n+ (the size of an output)) time. In the same situation, the fourth algorithm enumerates all maximum independent aets in O(n^2+ (the size of an output)) time. The first three algorithms are optimal to within a constant factor.