Abstract
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.
Work partially supported by the ESPRIT II Basic Research Actions Program of the EC under contract No. 3075 (Project ALCOM).
This work was done while the author was at Columbia University.
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© 1992 Springer-Verlag Berlin Heidelberg
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Italiano, G.F. (1992). Distributed algorithms for updating shortest paths. In: Toueg, S., Spirakis, P.G., Kirousis, L. (eds) Distributed Algorithms. WDAG 1991. Lecture Notes in Computer Science, vol 579. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0022448
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DOI: https://doi.org/10.1007/BFb0022448
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