Bicriteria network design problems

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The authors study a general class of bicriteria network design problems. A generic problem in this class is as follows: Given an undirected graph and two minimization objectives (under different cost functions), with a budget specified on the first, find a subgraph from a given subgraph class that minimizes the second objective subject to the budget on the first. They consider three different criteria -- the total edge cost, the diameter and the maximum degree of the network. Here, they present the first polynomial-time approximation algorithms for a large class of bicriteria network design problems for the above mentioned criteria. ... continued below

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29 p.

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Marathe, M.V.; Ravi, R.; Sundaram, R.; Ravi, S.S.; Rosenkrantz, D.J. & Hunt, H.B. III November 20, 1997.

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Description

The authors study a general class of bicriteria network design problems. A generic problem in this class is as follows: Given an undirected graph and two minimization objectives (under different cost functions), with a budget specified on the first, find a subgraph from a given subgraph class that minimizes the second objective subject to the budget on the first. They consider three different criteria -- the total edge cost, the diameter and the maximum degree of the network. Here, they present the first polynomial-time approximation algorithms for a large class of bicriteria network design problems for the above mentioned criteria. The following general types of results are presented. First, they develop a framework for bicriteria problems and their approximations. Second, when the two criteria are the same they present a black box parametric search technique. This black box takes in as input an (approximation) algorithm for the criterion situation and generates an approximation algorithm for the bicriteria case with only a constant factor loss in the performance guarantee. Third, when the two criteria are the diameter and the total edge costs they use a cluster based approach to devise approximation algorithms. The solutions violate both the criteria by a logarithmic factor. Finally, for the class of treewidth-bounded graphs, they provide pseudopolynomial-time algorithms for a number of bicriteria problems using dynamic programming. The authors show how these pseudopolynomial-time algorithms can be converted to fully polynomial-time approximation schemes using a scaling technique.

Physical Description

29 p.

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OSTI as DE98004329

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  • Other Information: PBD: 20 Nov 1997

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  • Other: DE98004329
  • Report No.: LA-UR--97-5200
  • Grant Number: W-7405-ENG-36
  • DOI: 10.2172/645490 | External Link
  • Office of Scientific & Technical Information Report Number: 645490
  • Archival Resource Key: ark:/67531/metadc695052

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Office of Scientific & Technical Information Technical Reports

Reports, articles and other documents harvested from the Office of Scientific and Technical Information.

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  • November 20, 1997

Added to The UNT Digital Library

  • Aug. 14, 2015, 8:43 a.m.

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  • Aug. 23, 2016, 2:54 p.m.

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Marathe, M.V.; Ravi, R.; Sundaram, R.; Ravi, S.S.; Rosenkrantz, D.J. & Hunt, H.B. III. Bicriteria network design problems, report, November 20, 1997; New Mexico. (digital.library.unt.edu/ark:/67531/metadc695052/: accessed November 18, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.