Paper in proceedings, 2002

We study powers of certain geometric intersection graphs: interval graphs, m-trapezoid graphs and circular-arc graphs. We define the pseudo product, (G,G′) → G * G′, of two graphs G and G′ on the same set of vertices, and show that G*G′ is contained in one of the three classes of graphs mentioned here above, if both G and G′ 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 G k if k ≥ 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.

Chalmers, Department of Computing Science

03029743 (ISSN) 16113349 (eISSN)

Vol. 2368 140-149Computer and Information Science

10.1007/3-540-45471-3_15

978-3-540-43866-3