A new bound for the 2-edge connected subgraph problem

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Given a complete undirected graph with non-negative costs on the edges, the 2-Edge Connected Subgraph Problem consists in finding the minimum cost spanning 2-edge connected subgraph (where multi-edges are allowed in the solution). A lower bound for the minimum cost 2-edge connected subgraph is obtained by solving the linear programming relaxation for this problem, which coincides with the subtour relaxation of the traveling salesman problem when the costs satisfy the triangle inequality. The simplest fractional solutions to the subtour relaxation are the 1/2-integral solutions in which every edge variable has a value which is a multiple of 1/2. The authors ... continued below

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16 p.

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Carr, R. & Ravi, R. April 1, 1998.

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  • Carr, R. Sandia National Labs., Albuquerque, NM (United States)
  • Ravi, R. Carnegie Mellon Univ., Pittsburgh, PA (United States)

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  • Sandia National Laboratories
    Publisher Info: Sandia National Labs., Albuquerque, NM (United States)
    Place of Publication: Albuquerque, New Mexico

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Description

Given a complete undirected graph with non-negative costs on the edges, the 2-Edge Connected Subgraph Problem consists in finding the minimum cost spanning 2-edge connected subgraph (where multi-edges are allowed in the solution). A lower bound for the minimum cost 2-edge connected subgraph is obtained by solving the linear programming relaxation for this problem, which coincides with the subtour relaxation of the traveling salesman problem when the costs satisfy the triangle inequality. The simplest fractional solutions to the subtour relaxation are the 1/2-integral solutions in which every edge variable has a value which is a multiple of 1/2. The authors show that the minimum cost of a 2-edge connected subgraph is at most four-thirds the cost of the minimum cost 1/2-integral solution of the subtour relaxation. This supports the long-standing 4/3 Conjecture for the TSP, which states that there is a Hamilton cycle which is within 4/3 times the cost of the optimal subtour relaxation solution when the costs satisfy the triangle inequality.

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16 p.

Notes

OSTI as DE98004529

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  • 6. conference on integer programming and combinatorial optimization, Houston, TX (United States), 22-24 Jun 1998

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  • Other: DE98004529
  • Report No.: SAND--98-0820C
  • Report No.: CONF-980633--
  • Grant Number: AC04-94AL85000
  • Office of Scientific & Technical Information Report Number: 671991
  • Archival Resource Key: ark:/67531/metadc708326

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Creation Date

  • April 1, 1998

Added to The UNT Digital Library

  • Sept. 12, 2015, 6:31 a.m.

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  • April 13, 2016, 4:03 p.m.

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Carr, R. & Ravi, R. A new bound for the 2-edge connected subgraph problem, article, April 1, 1998; Albuquerque, New Mexico. (digital.library.unt.edu/ark:/67531/metadc708326/: accessed December 10, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.