An Experimental Study of Algorithms for Packing Arborescences

Abstract

A classic result of Edmonds states that the maximum number of edge-disjoint arborescences of a directed graph G , rooted at a designated vertex s , equals the minimum cardinality c G ( s ) of an s -cut of G . This concept is related to the edge connectivity λ ( G ) of a strongly connected directed graph G , defined as the minimum number of edges whose deletion leaves a graph that is not strongly connected. In this paper, we address the question of how efficiently we can compute a maximum packing of edge-disjoint arborescences in practice, compared to the time required to determine the edge connectivity of a graph. To that end, we explore the design space of efficient algorithms for packing arborescences of a directed graph in practice and conduct a thorough empirical study to highlight the merits and weaknesses of each technique. In particular, we present an efficient implementation of Gabow’s arborescence packing algorithm and provide a simple but efficient heuristic that significantly improves its running time in practice. Project FANTA (eFficient Algorithms for NeTwork Analysis), number HFRI-FM17-431. H = G − A , and a complete ( k − 1)-intersection T for s on G . It uses the following key concept. An enlarging path consists of an edge e ∈ E + ( A ), and if e ∈ T , an augmenting path P for the ( k − 1)-intersection T − e on H − e . Gabow shows that if V ( A ) ̸ = V ( G ), then there is always an enlarging path.