Strengthening Integrality Gaps for Capacitated Network Design and Covering Problems

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A capacitated covering IP is an integer program of the form min{l_brace}ex{vert_bar}Ux {ge} d, 0 {le} x {le} b, x {element_of} Z{sup +}{r_brace}, where all entries of c, U, and d are nonnegative. Given such a formulation, the ratio between the optimal integer solution and the optimal solution to the linear program relaxation can be as bad as {parallel}d{parallel}{sub {proportional_to}}, even when U consists of a single row. They show that by adding additional inequalities, this ratio can be improved significantly. In the general case, they show that the improved ratio is bounded by the maximum number of non-zero coefficients ... continued below

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12 p.

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Carr, Robert D.; Fleischer, Lisa K.; Leung, Vitus J. & Phillips, Cynthia A. July 28, 1999.

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This article is part of the collection entitled: Office of Scientific & Technical Information Technical Reports and was provided by UNT Libraries Government Documents Department to Digital Library, a digital repository hosted by the UNT Libraries. It has been viewed 26 times . More information about this article can be viewed below.

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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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A capacitated covering IP is an integer program of the form min{l_brace}ex{vert_bar}Ux {ge} d, 0 {le} x {le} b, x {element_of} Z{sup +}{r_brace}, where all entries of c, U, and d are nonnegative. Given such a formulation, the ratio between the optimal integer solution and the optimal solution to the linear program relaxation can be as bad as {parallel}d{parallel}{sub {proportional_to}}, even when U consists of a single row. They show that by adding additional inequalities, this ratio can be improved significantly. In the general case, they show that the improved ratio is bounded by the maximum number of non-zero coefficients in a row of U, and provide a polynomial-time approximation algorithm to achieve this bound. This improves upon the results of Bertsimas and Vohra, strengthening their extension of Hall and Hochbaum.

Physical Description

12 p.

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OSTI as DE00009674

Medium: P; Size: 12 pages

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  • 11th Annual ACM-SIAM Symposium on Discrete Algorithms, San Francisco, CA (US), 01/09/2000--01/11/2000

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  • Report No.: SAND99-1972C
  • Grant Number: AC04-94AL85000
  • Office of Scientific & Technical Information Report Number: 9674
  • Archival Resource Key: ark:/67531/metadc793960

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  • July 28, 1999

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  • Dec. 19, 2015, 7:14 p.m.

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  • April 6, 2017, 8:10 p.m.

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Carr, Robert D.; Fleischer, Lisa K.; Leung, Vitus J. & Phillips, Cynthia A. Strengthening Integrality Gaps for Capacitated Network Design and Covering Problems, article, July 28, 1999; Albuquerque, New Mexico. (digital.library.unt.edu/ark:/67531/metadc793960/: accessed December 11, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.