An Efficient Scaling Algorithm for the Minimum Weight Bibranching Problem

Abstract

Let G = (VG, AG) be a digraph and let $S \sqcup T$ be a bipartition of VG. A bibranching is a subset B ⊆ AG such that for each node s ∈ S there exists a directed s–T path in B and, vice versa, for each node t ∈ T there exists a directed S–t path in B.

Bibranchings generalize both branchings and bipartite edge covers. Keijsper and Pendavingh proposed a strongly polynomial primal-dual algorithm that finds a minimum weight bibranching in O(n′(m + n logn)) time (where , , ).

In this paper we develop a weight-scaling $O(m \sqrt{n} \; \log n \log(nW))$-time algorithm for the minimum weight bibranching problem (where W denotes the maximum magnitude of arc weights).