Distributed algorithms for the quickest path problem

Hung, Y.-C. and G.-H. Chen, Distributed algorithms for the quickest path problem, Parallel Computing 18 (1992) 823-834. Let N=(V, A, C, L) be a network with node set V, arc set A, positive arc capacity function C, and nonnegative arc lead time function L. The quickest path problem is to find paths in N to transmit a given amount of data such that the transmission time is minimized. In this paper, distributed algorithms are developed for the quickest path problem in an asynchronous communication network. For the one-source quickest path problem, we present three algorithms that require O(rn 2) messages and O(rn 2) time, O(rmn) messages and O(rn) time, and O(rm T M log w) messages and O(rn T M log w) time for any E, 0 <E < 1, respectively, where m -I A I, n = I Vh r is the number of distinct capacity values of N, and w is the maximal arc weight of N. For the all-pairs quickest path problem, we present an algorithm that requires O(mn) messages and O(m) time.