An Algorithm for Minimum Cost Arc-Connectivity Orientations

Given a 2k-edge-connected undirected graph, we consider to find a minimum cost orientation that yields a k-arc-connected directed graph. This minimum cost k-arc-connected orientation problem is a special case of the submodular flow problem. Frank (1982) devised a combinatorial algorithm that solves the problem in O(k2 n3 m) time, where n and m are the numbers of vertices and edges, respectively. Gabow (1995) improved Frank's algorithm to run in O(kn2 m) time by introducing a new sophisticated data structure. We describe an algorithm that runs in O(k3 n3 + kn2 m) time without using sophisticated data structures. In addition, we present an application of the algorithm to find a shortest dijoin in O(n2 m) time, which matches the current best bound. Key Words. Arc-connectivity, Graph orientation, Submodular flow , Crossing family, Dijoin.

• Type: Journal
• Year: 2010
• Where: ALGORITHMICA
• Authors: Satoru Iwata, Yusuke Kobayashi
• Keywords: 2k-edge-connected Undirected Graph, ALGORITHMICA 2010, K-arc-connected Directed Graph, Minimum Cost Orientation