a new o(m + kn log d) algorithm to find the k shortest paths in acyclic digraphs

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 show that itsworst-case complexity is o(m + kn log d) in which n is the number ofnodes and m is the number of arcs and d is the mean degree of thegraph. the algorithm has a space complexity of o(nk). an experimental evaluation of t*is presented which confirm the advantage of our algorithm comparedto the most efficient k shortest paths algorithms known so far.