Abstract
We propose a fully-dynamic distributed algorithm for the all-pairs shortest paths problem on general networks with positive real edge weights. If Δσ 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 (nΔσ)in the worst case, where n is the number of nodes of the network. If \(\Delta_{\sigma} = o~(n^2)\), this is better than recomputing everything from scratch after each edge modification.
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