1 research outputs found
Quickest paths: faster algorithms and dynamization
Given a network , where , and , is a directed graph, is the capacity and is the lead time (or delay) for each edge , the quickest path problem is to find a path for a given source--destination pair such that the total lead time plus the inverse of the minimum edge capacity of the path is minimal. The problem has applications to fast data transmissions in communication networks. The best previous algorithm for the single pair quickest path problem runs in time , where is the number of distinct capacities of . In this paper, we present algorithms for general, sparse and planar networks that have significantly lower running times. For general networks, we show that the time complexity can be reduced to , where is at most the number of capacities greater than the capacity of the shortest (with respect to lead time) path in . For sparse networks, we present an algorithm with time complexity , where is a topological measure of . Since for sparse networks ranges from up to , this constitutes an improvement over the previously known bound of in all cases that . For planar networks, the complexity becomes . Similar improvements are obtained for the all--pairs quickest path problem. We also give the first algorithm for solving the dynamic quickest path problem