I/O-efficient topological sorting of planar DAGs

Abstract

We present algorithms that solve a number of fundamental problems on planar directed graphs (planar digraphs) in O((N)) I/Os, where (N) is the number of I/Os needed to sort N elements. The problems we consider are breadth-first search, the single-source shortest path problem, computing a directed ear decomposition of a strongly connected planar digraph, computing an open directed ear decomposition of a strongly connected biconnected planar digraph, and topologically sorting a planar directed acyclic graph.