The disjoint shortest paths problem

The Directed Disjoint Shortest Paths Problem

In the k disjoint shortest paths problem (k-DSPP), we are given a graph and its vertex pairs (s1, t1), . . . , (sk, tk), and the objective is to find k pairwise disjoint paths P1, . . . , Pk such that each path Pi is a shortest path from si to ti, if they exist. If the length of each edge is equal to zero, then this problem amounts to the disjoint paths problem, which is one of the well-studied...

The Disjoint Paths Problem

On the disjoint paths problem

On Shortest Disjoint Paths in Planar Graphs

For a graph G and a collection of vertex pairs {(s1, t1), . . . , (sk, tk)}, the k disjoint paths problem is to find k vertex-disjoint paths P1, . . . , Pk, where Pi is a path from si to ti for each i = 1, . . . , k. In the corresponding optimization problem, the shortest disjoint paths problem, the vertex-disjoint paths Pi have to be chosen such that a given objective function is minimized. We...

Shortest node-disjoint paths on random graphs

A localized method to distribute paths on random graphs is devised, aimed at finding the shortest paths between given source/destination pairs while avoiding path overlaps at nodes. We propose a method based on message-passing techniques to process global information and distribute paths optimally. Statistical properties such as scaling with system size and number of paths, average path-length ...