On External-Memory Planar Depth First Search

Abstract

Even though a large number of I/O-efficient graph algorithms have been developed, a number of fundamental problems still remain open. For example, no space- and I/O-efficient algorithms are known for depth-first search or breath-first search in sparse graphs. In this paper, we present two new results on I/O-efficient depth-first search in an important class of sparse graphs, namely undirected embedded planar graphs. We develop a new depth-first search algorithm that uses O(sort(N)log(N/M)) I/Os, and show how planar depth-first search can be reduced to planar breadth-first search in O(sort(N)) I/Os. As part of the first result, we develop the first I/O-efficient algorithm for finding a simple cycle separator of an embedded biconnected planar graph. This algorithm uses O(sort(N)) I/Os.