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 takeo(k logn) time, wherek is the number of edges in the path andn is the number of vertices in the graph. The first strategy takesO (k+logn) time to extract a requested shortest path. A second strategy takes Θ(k) time on average, assuming alln(n−1) shortest paths are equally likely to be requested. Both strategies introduce techniques for storing collections of disjoint intervals over the integers from 1 ton, so that identifying the interval within which a given integer falls can be performed quickly.
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