External-Memory Breadth-First Search with Sublinear I/O

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 ?(n + n+m/D?B ? logM/B n+m/B) 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 O(?n?(n+m)/D?B + n+m/D?B ? logM/B n+m/B)I/Os. Hence, for m = O(n) and all realistic values of logM/B n+m/B, it improves upon the I/O-performance of the best previous algorithm by a factor ?(?D ? B). 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.