On k-edge-connectivity problems with sharpened triangle inequality

  • Authors:

  • Hans-Joachim Böckenhauer;Dirk Bongartz;Juraj Hromkovič;Ralf Klasing;Guido Proietti;Sebastian Seibert;Walter Unger

  • Affiliations:

  • Lehrstuhl für Informatik I, RWTH Aachen, Aachen, Germany;Lehrstuhl für Informatik I, RWTH Aachen, Aachen, Germany;Lehrstuhl für Informatik I, RWTH Aachen, Aachen, Germany;CNRS, INRIA, Sophia-Antipolis, France;Dipartimento di Informatica, Università di L'Aquila, L'Aquila, Italy and Istituto di Analisi dei Sistemi ed Informatica "Antonio Ruberti", CNR, Roma, Italy;Lehrstuhl für Informatik I, RWTH Aachen, Aachen, Germany;Lehrstuhl für Informatik I, RWTH Aachen, Aachen, Germany

  • Venue:
  • CIAC'03 Proceedings of the 5th Italian conference on Algorithms and complexity
  • Year:
  • 2003

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Abstract

The edge-connectivityproblem is to find a minimum-cost k-edge-connected spanning subgraph of an edge-weighted, undirected graph G for any given G and k. Here we consider its APX-hard subproblems with respect to the parameter β, with 1/2 ≤ β G = (V, E) is a complete graph with a cost function c satisfying the sharpened triangle inequality c({u, v}) ≤ β ċ (c({u, w}) + c({w, v})) for all u, v, w ∈ V. First, we give a linear-time approximation algorithm for these optimization problems with approximation ratio β/1-β for any 1/2 ≤ β k. The result above is based on a rough combinatorial argumentation. We sophisticate our combinatorial consideration in order to design a (1 + 5(2β-1)/9(1-β))- approximation algorithm for the 3-edge-connectivitysubgraph problem for graphs satisfying the sharpened triangle inequality for 1/2 ≤ β ≤ 2/3.