A Fully Dynamic Algorithm for Distributed Shortest Paths

We propose a fully-dynamic distributed algorithm for the all-pairs shortest paths problem on general networks with positive real edge weights. If ∆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(n∆σ) in the worst case, where n is the number of nodes of the network. If ∆σ = o(n2), 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. ∗Dipartimento di Ingegneria Elettrica, Università dell’Aquila, I-67040 Monteluco di Roio L’Aquila, Italy. E-mail: [email protected], [email protected], [email protected] †Dipartimento di Informatica e Sistemistica, Università di Roma “La Sapienza”, via Salaria 113, I-00198 Roma, Italy. E-mail: [email protected]