Distributed algorithms for updating shortest paths
We present a distributed algorithm for updating all pairs shortest paths when an edge is either inserted or has its cost decreased. For unit edge costs (i.e., for maintaining all pairs minimum hops) our algorithm transmits a total of O(V3 log V) messages during the insertion of O(V2) edges. This gives basically O(V log V) messages per change in the amortized sense. For integer edge costs in [1, W], our algorithm transmits at most O(WV3 log(VW)) messages during O(WV2) edge insertions or edge cost decreases. Again, this gives O(V log(VW)) messages per change in the amortized sense. The algorithm runs asynchronously, requires O(V) time per change and O(V) space per node.
This result favorably compares to using the best known distributed algorithm for computing all pairs shortest paths from scratch, and to other dynamic distributed algorithms previously proposed in the literature.
KeywordsShort Path Sequential Algorithm Message Complexity Edge Cost Good Pair
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