Finding K shortest looping paths with waiting time in a time–window network

Finding K shortest looping paths in a traffic-light network

In this paper we consider a tra$c-light network where every node in the network is associated with the constraint consisting of a repeated sequence of time windows. The constraint aims to simulate the operations of tra$c-light control in an intersection of roads. With this kind of constraints in place, directions of routes when passing through the intersections can be formally modeled. The obje...

Finding the k Shortest Paths

We give algorithms for finding the k shortest paths (not required to be simple) connecting a pair of vertices in a digraph. Our algorithms output an implicit representation of these paths in a digraph with n vertices and m edges, in time O(m + n log n + k). We can also find the k shortest paths from a given source s to each vertex in the graph, in total time O(m+ n log n+ kn). We describe appli...

Finding the k Shortest Paths in

A concurrent-read exclusive-write PRAM algorithm is developed to nd the k shortest paths between pairs of vertices in an edge-weighted directed graph. Repetitions of vertices along the paths are allowed. The algorithm computes an implicit representation of the k shortest paths to a given destination vertex from every vertex of a graph with n vertices and m edges, using O(m + nk log 2 k) work an...

Finding k Simple Shortest Paths and Cycles

We present algorithms and hardness results for several problems related to finding multiple simple shortest paths in a graph. Our main result is a new algorithm for finding k simple shortest paths for all pairs of vertices in a weighted directed graph G = (V,E). For k = 2 our algorithm runs in O(mn + n logn) time where m and n are the number of edges and vertices in G. Our approach is based on ...

Time - Varying K Shortest Paths