I/O-Efficient algorithms on near-planar graphs

Authors:
Herman Haverkort;Laura Toma
Affiliations:
Department of Computing Science, Eindhoven University of Technology, Eindhoven, The Netherlands;Department of Computer Science, Bowdoin College, Brunswick, ME, United States of America
Venue:
LATIN'06 Proceedings of the 7th Latin American conference on Theoretical Informatics
Year:
2006

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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.