I/O-Efficient Algorithms on Near-Planar Graphs

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.