A New Bound for the Ration Between the 2-Matching Problem and Its Linear Programming Relaxation

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Description

Consider the 2-matching problem defined on the complete graph, with edge costs which satisfy the triangle inequality. We prove that the value of a minimum cost 2-matching is bounded above by 4/3 times the value of its linear programming relaxation, the fractional 2-matching problem. This lends credibility to a long-standing conjecture that the optimal value for the traveling salesman problem is bounded above by 4/3 times the value of its linear programming relaxation, the subtour elimination problem.

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21 p.

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Boyd, Sylvia & Carr, Robert July 28, 1999.

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

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Description

Consider the 2-matching problem defined on the complete graph, with edge costs which satisfy the triangle inequality. We prove that the value of a minimum cost 2-matching is bounded above by 4/3 times the value of its linear programming relaxation, the fractional 2-matching problem. This lends credibility to a long-standing conjecture that the optimal value for the traveling salesman problem is bounded above by 4/3 times the value of its linear programming relaxation, the subtour elimination problem.

Physical Description

21 p.

Notes

OSTI as DE00009490

Medium: P; Size: 21 pages

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  • Journal Name: Mathematical Programming; Other Information: Submitted to Mathematical Programming

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  • Report No.: SAND99-1971J
  • Grant Number: AC04-94AL85000
  • Office of Scientific & Technical Information Report Number: 9490
  • Archival Resource Key: ark:/67531/metadc794143

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  • July 28, 1999

Added to The UNT Digital Library

  • Dec. 19, 2015, 7:14 p.m.

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  • April 7, 2017, 7:25 p.m.

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Boyd, Sylvia & Carr, Robert. A New Bound for the Ration Between the 2-Matching Problem and Its Linear Programming Relaxation, article, July 28, 1999; Albuquerque, New Mexico. (digital.library.unt.edu/ark:/67531/metadc794143/: accessed September 23, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.