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′) → 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.
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Agnarsson, G., Damaschke, P., Halldórsson, M.M. (2002). Powers of Geometric Intersection Graphs and Dispersion Algorithms. In: Penttonen, M., Schmidt, E.M. (eds) Algorithm Theory — SWAT 2002. SWAT 2002. Lecture Notes in Computer Science, vol 2368. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45471-3_15
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DOI: https://doi.org/10.1007/3-540-45471-3_15
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