I/O-Efficient Undirected Shortest Paths with Unbounded Edge Lengths

We show how to compute single-source shortest paths in undirected graphs with non-negative edge lengths in O(√nm/Blogn+MST(n,m)I/Os, where n is the number of vertices, m is the number of edges, B is the disk block size, and MST(n,m) is the I/O-cost of computing a minimum spanning tree. For sparse graphs, the new algorithm performs O((n/√B)logn) I/Os. This result removes our previous algorithm's dependence on the edge lengths in the graph.

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