Algorithms for the quickest path problem and the enumeration of quickest paths

Let N = (V, R, e, I) be an input network with node set V, arc set A, positive arc weight function c and nonnegative arc weight function 1. Let u be the amount of data to be transmitted. The quickest path problem is to find a routing path in N to transmit the given amount of data in minimum time. In a recent paper, Chen and Chin proposed this problem and developed algorithms for the single pair quickest path problem with time complexity O(re + rn log n). where n = lVl, e = IAl, and r is the number of distinct capacity vahres of N. In this paper, we first develop an alternative algorithm for the single pair quickest path problem with same time complexity and less space ~ui~ent. We then study the constrained quickest path problem and propose an O(re + m log n) time algorithm. Finally, we develop an algorithm to enumerate the first m quickest paths to send a given amount of data from one node to another with time complexity O(rmne + rtnn2 log n).