Multicriteria approximation through decomposition

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The authors propose a general technique called solution decomposition to devise approximation algorithms with provable performance guarantees. The technique is applicable to a large class of combinatorial optimization problems that can be formulated as integer linear programs. Two key ingredients of the technique involve finding a decomposition of a fractional solution into a convex combination of feasible integral solutions and devising generic approximation algorithms based on calls to such decompositions as oracles. The technique is closely related to randomized rounding. The method yields as corollaries unified solutions to a number of well studied problems and it provides the first approximation ... continued below

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19 p.

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Burch, C.; Krumke, S.; Marathe, M.; Phillips, C. & Sundberg, E. December 1, 1997.

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  • Burch, C. Carnegie Mellon Univ., Pittsburgh, PA (United States). School of Computer Sciences
  • Krumke, S. Univ. of Wuerzburg (Germany). Dept. of Computer Science
  • Marathe, M. Los Alamos National Lab., NM (United States)
  • Phillips, C. Sandia National Labs., Albuquerque, NM (United States). Applied Mathematics Dept.
  • Sundberg, E. Rutgers Univ., NJ (United States). Dept. of Computer Science

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Description

The authors propose a general technique called solution decomposition to devise approximation algorithms with provable performance guarantees. The technique is applicable to a large class of combinatorial optimization problems that can be formulated as integer linear programs. Two key ingredients of the technique involve finding a decomposition of a fractional solution into a convex combination of feasible integral solutions and devising generic approximation algorithms based on calls to such decompositions as oracles. The technique is closely related to randomized rounding. The method yields as corollaries unified solutions to a number of well studied problems and it provides the first approximation algorithms with provable guarantees for a number of new problems. The particular results obtained in this paper include the following: (1) The authors demonstrate how the technique can be used to provide more understanding of previous results and new algorithms for classical problems such as Multicriteria Spanning Trees, and Suitcase Packing. (2) They show how the ideas can be extended to apply to multicriteria optimization problems, in which they wish to minimize a certain objective function subject to one or more budget constraints. As corollaries they obtain first non-trivial multicriteria approximation algorithms for problems including the k-Hurdle and the Network Inhibition problems.

Physical Description

19 p.

Notes

OSTI as DE98001686

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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: DE98001686
  • Report No.: SAND--97-3087C
  • Report No.: CONF-980633--
  • Grant Number: AC04-94AL85000;W-7405-ENG-36
  • Office of Scientific & Technical Information Report Number: 642754
  • Archival Resource Key: ark:/67531/metadc689718

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  • December 1, 1997

Added to The UNT Digital Library

  • Aug. 14, 2015, 8:43 a.m.

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  • July 28, 2016, 7:18 p.m.

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Burch, C.; Krumke, S.; Marathe, M.; Phillips, C. & Sundberg, E. Multicriteria approximation through decomposition, article, December 1, 1997; Albuquerque, New Mexico. (digital.library.unt.edu/ark:/67531/metadc689718/: accessed August 17, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.