Approximating the smallest 2-vertex connected spanning subgraph of a directed graph

  • Authors:

  • Loukas Georgiadis

  • Affiliations:

  • Department of Informatics and Telecommunications Engineering, University of Western Macedonia, Greece

  • Venue:
  • ESA'11 Proceedings of the 19th European conference on Algorithms
  • Year:
  • 2011

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Abstract

We consider the problem of approximating the smallest 2- vertex connected spanning subgraph (2-VCSS) of a 2-vertex connected directed graph, and explore the efficiency of fast heuristics. First, we present a linear-time heuristic that gives a 3-approximation of the smallest 2-VCSS. Then we show that this heuristic can be combined with an algorithm of Cheriyan and Thurimella that achieves a (1 + 1/k)- approximation of the smallest k-VCSS. The combined algorithm preserves the 1.5 approximation guarantee of the Cheriyan-Thurimella algorithm for k = 2 and improves its running time from O(m2) to O(m√n + n2), for a digraph with n vertices and m arcs. Finally, we present an experimental evaluation of the above algorithms for a variety of input data. The experimental results show that our linear-time heuristic achieves in practice a much better approximation ratio than 3, suggesting that a tighter analysis may be possible. Furthermore, the experiments show that the combined algorithm not only improves the running time of the Cheriyan-Thurimella algorithm, but it may also compute a smaller 2-VCSS.