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.
Research supported in part by the MIUR project AlgoDEEP prot. 2008TFBWL4.
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Di Giacomo, E., Didimo, W., Liotta, G., Montecchiani, F. (2012). h-Quasi Planar Drawings of Bounded Treewidth Graphs in Linear Area. In: Golumbic, M.C., Stern, M., Levy, A., Morgenstern, G. (eds) Graph-Theoretic Concepts in Computer Science. WG 2012. Lecture Notes in Computer Science, vol 7551. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-34611-8_12
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DOI: https://doi.org/10.1007/978-3-642-34611-8_12
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