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On k-Edge-Connectivity Problems with Sharpened Triangle Inequality

Extended Abstract
  • Hans-Joachim Böckenhauer
  • Dirk Bongartz
  • Juraj Hromkovič
  • Ralf Klasing
  • Guido Proietti
  • Sebastian Seibert
  • Walter Unger
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2653)

Abstract

The edge-connectivity problem 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 \( \frac{1} {2} \)β < 1, where G = (V, E) is a complete graph with a cost function c satisfying the sharpened triangle inequality
$$ c\left( {\left\{ {u,v} \right\}} \right) \leqslant \beta .\left( {c\left\{ {u,w} \right\}} \right) + c\left( {\left\{ {w,v} \right\}} \right) $$
for all u, v, wV.

First, we give a linear-time approximation algorithm for these optimization problems with approximation ratio \( \frac{\beta } {{1 - \beta }} \) for any \( \frac{1} {2} \)β < 1, which does not depend on k.

The result above is based on a rough combinatorial argumentation. We sophisticate our combinatorial consideration in order to design a \( \left( {1 + \frac{{5\left( {2\beta - 1} \right)}} {{9\left( {1 - \beta } \right)}}} \right) \) approximation algorithm for the 3-edge-connectivity subgraph problem for graphs satisfying the sharpened triangle inequality for \( \frac{1} {2} \)β\( \frac{2} {3} \) .

Keywords

Approximation Algorithm Triangle Inequality Approximation Ratio Travel Salesman Problem Hamiltonian Cycle 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Hans-Joachim Böckenhauer
    • 1
  • Dirk Bongartz
    • 1
  • Juraj Hromkovič
    • 1
  • Ralf Klasing
    • 2
  • Guido Proietti
    • 3
    • 4
  • Sebastian Seibert
    • 1
  • Walter Unger
    • 1
  1. 1.Lehrstuhl für Informatik IRWTH AachenAachenGermany
  2. 2.Project MASCOTTECNRS/INRIASophia-AntipolisFrance
  3. 3.Dipartimento di InformaticaUniversità di L’AquilaL’AquilaItaly
  4. 4.Istituto di Analisi dei Sistemi ed Informatica “Antonio Ruberti”CNRRomaItaly

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