On External-Memory Planar Depth First Search

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 spaceand 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 breadthfirst 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. Communicated by Giuseppe Liotta and Ioannis G. Tollis: submitted November 2002; revised January 2003. Lars Arge and Laura Toma supported in part by the National Science Foundation through ESS grant EIA–9870734, RI grant EIA–9972879 and CAREER grant CCR– 9984099. Ulrich Meyer supported in part by the IST Programme of the EU under contract number IST–1999–14186 (ALCOM–FT). Norbert Zeh supported in part by NSERC and NCE GEOIDE research grants. L. Arge et al., On External-Memory Planar DFS , JGAA, 7(2) 105–129 (2003)106