The quickest path problem in distributed computing systems
Let N=(V, A, C, L) be an input 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 a path 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 two algorithms that require O(rn2) messages, O(rn2) time, and O(rmn) messages, O(rn) time, respectively, where m=¦A¦, n=¦V ¦, and r is the number of distinct capacity values of N. For the all-pairs quickest path problem, we present an algorithm that requires O(mn) messages and O(m) time.
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