Abstract
We propose a fully dynamic distributed algorithm for the all-pairs shortest paths problem on general networks with positive real edge weights. If Δ σ is the number of pairs of nodes changing the distance after a single edge modification σ ( insert, delete, weight decrease, or weight increase) then the message complexity of the proposed algorithm is O( nΔ σ ) in the worst case, where n is the number of nodes of the network. If Δ σ = o(n 2) , this is better than recomputing everything from scratch after each edge modification. Up to now only a result of Ramarao and Venkatesan was known, stating that the problem of updating shortest paths in a dynamic distributed environment is as hard as that of computing shortest paths.
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