we give an algorithm, called t*, for finding the k shortest simplepaths connecting a certain pair of nodes, s and t, in a acyclic digraph.first the nodes of the graph are labeled according to the topologicalordering. then for node i an ordered list of simple s − i paths iscreated. the length of the list is at most k and it is created by usingtournament trees. we prove the correctness of t* and ...

Numerous algorithms have been proposed to solve the shortest-pathproblem; many of them consider a single-mode network and crispcosts. Other attempts have addressed the problem of fuzzy costs ina single-mode network, the so-called fuzzy shortest-path problem(FSPP). The main contribution of the present work is to solve theoptimum path problem in a multimodal transportation network, inwhich the co...

We address the problem for finding the K best path trees connecting a source node with any other non-source node in a directed network with arbitrary lengths. The main result in this paper is the proof that the kth shortest path tree is adjacent to at least one of the previous (k−1) shortest path trees. Consequently, we design an O(+Km) time and O(K+m) space algorithm to determine the K shortes...

A graph has an optimaì-interval routing scheme if it is possible to direct messages along shortest paths by labeling each edge with at most`pairwise-disjoint subintervals of the cyclic interval 1 : : : n] (where each node of the graph is labeled by an integer in the range). Although much progress has been made for`= 1, there is as yet no general tight characterization of the classes of graphs a...

numerous algorithms have been proposed to solve the shortest-pathproblem; many of them consider a single-mode network and crispcosts. other attempts have addressed the problem of fuzzy costs ina single-mode network, the so-called fuzzy shortest-path problem(fspp). the main contribution of the present work is to solve theoptimum path problem in a multimodal transportation network, inwhich the co...

k-Interval Routing Scheme (k-IRS) is a compact routing method that allows up to k interval labels to be assigned to an arc; and global k-IRS allows not more than a total of k interval labels in the whole network. A fundamental problem is to characterize the networks that admit k-IRS (or global k-IRS). Many of the problems related to single-shortest-path k-IRS have already been shown to be NP-co...