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Title: Bicriteria network design problems

Abstract

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 logarithmicmore » 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.« less

Authors:
 [1];  [2];  [3]; ; ;  [4]
  1. Los Alamos National Lab., NM (United States)
  2. Princeton Univ., NJ (United States)
  3. Massachusetts Inst. of Tech., Cambridge, MA (United States)
  4. State Univ. of New York, Albany, NY (United States). Dept. of Computer Science
Publication Date:
Research Org.:
Los Alamos National Lab., NM (United States)
Sponsoring Org.:
USDOE, Washington, DC (United States); National Science Foundation, Washington, DC (United States); Defense Advanced Research Projects Agency, Arlington, VA (United States)
OSTI Identifier:
645490
Report Number(s):
LA-UR-97-5200
ON: DE98004329; CNN: Contract DARPA N0014-92-J-1799;Grant NSF CCR 92-12184;Grant NSF CCR 9625297;Grant NSF CCR 94-06611;Grant NSF CCR 90-06396; TRN: AHC2DT03%%31
DOE Contract Number:  
W-7405-ENG-36
Resource Type:
Technical Report
Resource Relation:
Other Information: PBD: 20 Nov 1997
Country of Publication:
United States
Language:
English
Subject:
99 MATHEMATICS, COMPUTERS, INFORMATION SCIENCE, MANAGEMENT, LAW, MISCELLANEOUS; COMPUTER NETWORKS; CAPITALIZED COST; COST ESTIMATION; PLANNING

Citation Formats

Marathe, M V, Ravi, R, Sundaram, R, Ravi, S S, Rosenkrantz, D J, and Hunt, III, H B. Bicriteria network design problems. United States: N. p., 1997. Web. doi:10.2172/645490.
Marathe, M V, Ravi, R, Sundaram, R, Ravi, S S, Rosenkrantz, D J, & Hunt, III, H B. Bicriteria network design problems. United States. https://doi.org/10.2172/645490
Marathe, M V, Ravi, R, Sundaram, R, Ravi, S S, Rosenkrantz, D J, and Hunt, III, H B. Thu . "Bicriteria network design problems". United States. https://doi.org/10.2172/645490. https://www.osti.gov/servlets/purl/645490.
@article{osti_645490,
title = {Bicriteria network design problems},
author = {Marathe, M V and Ravi, R and Sundaram, R and Ravi, S S and Rosenkrantz, D J and Hunt, III, H B},
abstractNote = {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.},
doi = {10.2172/645490},
url = {https://www.osti.gov/biblio/645490}, journal = {},
number = ,
volume = ,
place = {United States},
year = {1997},
month = {11}
}