I/O-efficient algorithms on near-planar graphs

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Abstract

Obtaining I/O-efficient algorithms for basic graph problems on sparse directed graphs is a long-standing open problem. While the best known upper bounds for most basic problems on such graphs with V vertices still require Ω(V) I/Os, optimal O(sort(V)) I/O algorithms are known for special classes of sparse graphs, like planar graphs and grid graphs, It is hard to accept that a problem becomes difficult as soon as the graph contains a few deviations from planarity. In this paper we extend the class of graphs on which basic graph problems can be solved I/O-efficiently. We give a characterization of near-planarity which covers a wide range of near-planar graphs, and obtain the first I/O-efficient algorithms for directed graphs that are near-planar. © Springer-Verlag Berlin Heidelberg 2006.

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Haverkort, H., & Toma, L. (2006). I/O-efficient algorithms on near-planar graphs. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 3887 LNCS, pp. 580–591). https://doi.org/10.1007/11682462_54

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