h-quasi planar drawings of bounded treewidth graphs in linear area

Authors:
Emilio Di Giacomo;Walter Didimo;Giuseppe Liotta;Fabrizio Montecchiani
Affiliations:
Dip. di Ingegneria Elettronica e dell'Informazione, Università degli Studi di Perugia, Italy;Dip. di Ingegneria Elettronica e dell'Informazione, Università degli Studi di Perugia, Italy;Dip. di Ingegneria Elettronica e dell'Informazione, Università degli Studi di Perugia, Italy;Dip. di Ingegneria Elettronica e dell'Informazione, Università degli Studi di Perugia, Italy
Venue:
WG'12 Proceedings of the 38th international conference on Graph-Theoretic Concepts in Computer Science
Year:
2012

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Abstract

We study the problem of computing h-quasi planar drawings in linear area; in an h-quasi planar drawing the number of mutually crossing edges is at most h−1. We prove that every n-vertex partial k-tree admits a straight-line h-quasi planar drawing in O(n) area, where h depends on k but not on n. For specific sub-families of partial k-trees, we present ad-hoc algorithms that compute h-quasi planar drawings in linear area, such that h is significantly reduced with respect to the general result. Finally, we compare the notion of h-quasi planarity with the notion of h-planarity, where each edge is allowed to be crossed at most h times.