Powers of Geometric Intersection Graphs and Dispersion Algorithms

Authors:
Geir Agnarsson;Peter Damaschke;Magnús M. Halldórsson
Affiliations:
-;-;-
Venue:
SWAT '02 Proceedings of the 8th Scandinavian Workshop on Algorithm Theory
Year:
2002

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Abstract

We study powers of certain geometric intersection graphs: interval graphs, m-trapezoid graphs and circular-arc graphs. We define the pseudo product, (G,G驴) 驴 G * G驴, of two graphs G and G驴 on the same set of vertices, and show that G*G驴 is contained in one of the three classes of graphs mentioned here above, if both G and G驴 are also in that class and fulfill certain conditions. This gives a new proof of the fact that these classes are closed under taking power; more importantly, we get efficient methods for computing the representation for Gk if k 驴 1 is an integer and G belongs to one of these classes, with a given representation sorted by endpoints. We then use these results to give efficient algorithms for the k-independent set, dispersion and weighted dispersion problem on these classes of graphs, provided that their geometric representations are given.