# Searching among intervals and compact routing tables

## 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/n*^{2}) 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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