Abstract

Shortest paths in weighted directed graphs are considered within the context of compact routing tables. Strategies are given for organizing compact routing tables so that extracting a requested shortest path will take o(k log n) time, where k is the number of edges in the path and n the number of vertices in the graph. The first strategy takes O(k+log n) time to extract a requested shortest path. A second strategy takes O(K/n2) average time, if all requested paths are equally likely, where K is the total number of edges (counting repetitions) in all n(n}-1) shortest paths. Both strategies introduce techniques for storing collections of disjoint intervals over the integers from 1 to n, so that identifying the interval within which a given integer falls can be performed quickly.

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