Finding Arc and Vertex-Disjoint Paths in Networks

Multipath Routing plays an important role in communication networks. Multiple disjoint paths can increase the effective bandwidth between pairs of vertices, avoid congestion in a network and reduce the probability of dropped packets. In this paper, we built mathematical models for arc-disjoint paths problem and vertex-disjoint paths problem respectively, and then proposed polynomial algorithms for finding the shortest pair of arc and vertex-disjoint paths, both with the time complexity of O(m). Furthermore, we extend these algorithms to find any k disjoint paths in time O(km), whose sum-weight is minimized.