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

The quickest path problem, which was originally proposed by Chen and Chin, is a variant of the shortest path problem. Its objective is to find quickest paths in a network to transmit a given amount of data such that the transmission time is minimized. If the quickest paths are required to go through a specified path, then the restricted problem is called the constrained quickest path problem. In this paper, for all pairs of nodes in a network N, an O(mn²) time algorithm is first presented to find constrained quickest paths, and then an O(k²mn²) time algorithm is presented to enumerate the first k quickest paths. The present results improve previous results by Rosen, Sun and Xue.