I/O-efficient shortest path algorithms for undirected graphs with random or bounded edge lengths

Abstract

We present I/O-efficient single-source shortest path algorithms for undirected graphs. Our main result is an algorithm with I/O complexity O(√( nm log L )/ B +MST( n, m )) on graphs with n vertices, m edges, and arbitrary edge lengths between 1 and L ; MST( n, m denotes the I/O complexity of computing a minimum spanning tree; B denotes the disk block size. If the edge lengths are drawn uniformly at random from (0,1], the expected I/O complexity of the algorithm is O(√ nm/B + ( m/B )log B + MST( n, m )). A simpler algorithm has expected I/O complexity O(√( nm log B )/ B + MST( n, m )) for uniformly random edge lengths.