External-memory Breadth-first search with sublinear I/O

Abstract

Breadth-first search (BFS) is a basic graph exploration technique. We give the first external memory algorithm for sparse undirected graphs with sublinear I/O. The best previous algorithm requires (formula presented) I/Os on a graph with n nodes and m edges and a machine with main-memory of size M, D parallel disks, and block size B. We present a new approach which requires only (formula presented) I/Os. Hence, for m = O(n) and all realistic values of (formula presented), it improves upon the I/O-performance of the best previous algorithm by a factor (formula presented). Our approach is fairly simple and we conjecture it to be practical. We also give improved algorithms for undirected single-source shortest-paths with small integer edge weights and for semi-external BFS on directed Eulerian graphs