Simplified External Memory Algorithms for Planar DAGs

In recent years a large number I/O-efficient algorithms have been developed for fundamental planar graph problems. Most of these algorithms rely on the existence of small planar separators as well as an O(sort(N)) I/O algorithm for computing a partition of a planar graph based on such separators, where O(sort(N)) is the number of I/Os needed to sort N elements. In this paper we simplify and unify several of the known planar graph results by developing linear I/O algorithms for the fundamental single-source shortest path, breadth-first search and topological sorting problems on planar directed acyclic graphs, provided that a partition is given; thus our results give O(sort(N)) I/Os algorithms for the three problems. While algorithms for all these problems were already known, the previous algorithms are all considerably more complicated than our algorithms and use Θ(sort(N)) I/Os even if a partition is known. Unlike the previous algorithm, our topological sorting algorithm is simple enough to be of practical interest.