Efficient distributed algorithms for computing shortest pairs of maximally disjoint paths in communication networks

Distributed algorithms are presented for finding two maximally disjoint paths of minimum total length from each possible source node to a destination, including both node-disjoint and link-disjoint versions of the algorithm. A synchronous algorithm having communication complexity O(|E|log D+||V|D) and time complexity O(|V|W), where |V| and |E| denote the number of nodes and links in G, W is the maximum link length, and D is the depth of a shortest-path spanning tree directed toward the destination, is presented. For the important case W=O(1), the time complexity becomes O(|V|). In this case, the asynchronous algorithm obtained by applying Synchronizer α of B. Awerbuch (1987) has communication complexity O(|E|V|) and time complexity O(|V|). Serial, centralized versions of the algorithms with time complexity O(|E|+|V| log |V|) and space complexity O(|E|) are also presented