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  All pairs lightest shortest paths (1999) [7 citations — 5 self]

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by Uri Zwick
In Proceedings of the 31th Annual ACM Symposium on Theory of Computing
http://www.math.tau.ac.il/~zwick/aplsp-STOC.ps.gz
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Abstract:

Two vertices in a weighted directed graph may be connected by many shortest paths. Although all these paths are shortest in terms of weight, the number of edges on them may vary substantially. This leads us to consider the All Pairs Lightest Shortest Paths (APLSP) problem. A solution to this problem is a representation of shortest paths between all of pairs of vertices in the graph such that each of these shortest paths uses a minimal, or a close to minimal, number of edges. We present the following algorithms for obtaining exact or approximate solutions to the APLSP problem: ffl An ~ O(n

Citations

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