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An Experimental Study of Algorithms for Packing Arborescences

Authors Loukas Georgiadis , Dionysios Kefallinos, Anna Mpanti, Stavros D. Nikolopoulos

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Author Details

Loukas Georgiadis
  • Department of Computer Science & Engineering, University of Ioannina, Greece
Dionysios Kefallinos
  • Department of Computer Science & Engineering, University of Ioannina, Greece
Anna Mpanti
  • Department of Computer Science & Engineering, University of Ioannina, Greece
Stavros D. Nikolopoulos
  • Department of Computer Science & Engineering, University of Ioannina, Greece


We would like to thank the anonymous referees for several useful comments.

Cite AsGet BibTex

Loukas Georgiadis, Dionysios Kefallinos, Anna Mpanti, and Stavros D. Nikolopoulos. An Experimental Study of Algorithms for Packing Arborescences. In 20th International Symposium on Experimental Algorithms (SEA 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 233, pp. 14:1-14:16, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022)


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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Graph algorithms analysis
  • Mathematics of computing → Graph algorithms
  • Arborescences
  • Edge Connectivity
  • Graph Algorithms


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