Searching among intervals and compact routing tables

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 is 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 Theta(k) time on average, assuming all n(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 to n, so that identifying the interval within which a given integer falls can be performed quickly.