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Title: Improving Steiner trees of a network under multiple constraints

Abstract

The authors consider the problem of decreasing the edge weights of a given network so that the modified network has a Steiner tree in which two performance measures are simultaneously optimized. They formulate these problems, referred to as bicriteria network improvement problems, by specifying a budget on the total modification cost, a constraint on one of the performance measures and using the other performance measure as a minimization objective. Network improvement problems are known to be NP-hard even when only one performance measure is considered. The authors present the first polynomial time approximation algorithms for bicriteria network improvement problems. The approximation algorithms are for two pairs of performance measures, namely (diameter, total cost) and (degree, total cost). These algorithms produce solutions which are within a logarithmic factor of the optimum value of the minimization objective while violating the constraints only by a logarithmic factor. The techniques also yield approximation schemes when the given network has bounded treewidth. Many of the approximation results can be extended to more general network design problems.

Authors:
;  [1];  [2];  [3];  [4]
  1. Univ. of Wuerzburg (Germany). Dept. of Computer Science
  2. Los Alamos National Lab., NM (United States)
  3. Carnegie Mellon Univ., Pittsburgh, PA (United States)
  4. State Univ. of New York, Albany, NY (United States). Dept. of Computer Science
Publication Date:
Research Org.:
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Sponsoring Org.:
USDOE, Washington, DC (United States)
OSTI Identifier:
251414
Report Number(s):
LA-UR-96-1374; CONF-960882-1
ON: DE96010936; TRN: AHC29614%%142
DOE Contract Number:  
W-7405-ENG-36
Resource Type:
Conference
Resource Relation:
Conference: 4. Europeoan symposium on algorithms, Corfu (Greece), Aug 1996; Other Information: PBD: [1996]
Country of Publication:
United States
Language:
English
Subject:
99 MATHEMATICS, COMPUTERS, INFORMATION SCIENCE, MANAGEMENT, LAW, MISCELLANEOUS; COMPUTER NETWORKS; COMPUTER-AIDED DESIGN; OPTIMIZATION; ALGORITHMS; DIAGRAMS; LIMITING VALUES; TRANSFORMATIONS; POLYNOMIALS; OPERATIONS RESEARCH

Citation Formats

Krumke, S O, Noltemeier, H, Marathe, M V, Ravi, R, and Ravi, S S. Improving Steiner trees of a network under multiple constraints. United States: N. p., 1996. Web.
Krumke, S O, Noltemeier, H, Marathe, M V, Ravi, R, & Ravi, S S. Improving Steiner trees of a network under multiple constraints. United States.
Krumke, S O, Noltemeier, H, Marathe, M V, Ravi, R, and Ravi, S S. 1996. "Improving Steiner trees of a network under multiple constraints". United States. https://www.osti.gov/servlets/purl/251414.
@article{osti_251414,
title = {Improving Steiner trees of a network under multiple constraints},
author = {Krumke, S O and Noltemeier, H and Marathe, M V and Ravi, R and Ravi, S S},
abstractNote = {The authors consider the problem of decreasing the edge weights of a given network so that the modified network has a Steiner tree in which two performance measures are simultaneously optimized. They formulate these problems, referred to as bicriteria network improvement problems, by specifying a budget on the total modification cost, a constraint on one of the performance measures and using the other performance measure as a minimization objective. Network improvement problems are known to be NP-hard even when only one performance measure is considered. The authors present the first polynomial time approximation algorithms for bicriteria network improvement problems. The approximation algorithms are for two pairs of performance measures, namely (diameter, total cost) and (degree, total cost). These algorithms produce solutions which are within a logarithmic factor of the optimum value of the minimization objective while violating the constraints only by a logarithmic factor. The techniques also yield approximation schemes when the given network has bounded treewidth. Many of the approximation results can be extended to more general network design problems.},
doi = {},
url = {https://www.osti.gov/biblio/251414}, journal = {},
number = ,
volume = ,
place = {United States},
year = {Mon Jul 01 00:00:00 EDT 1996},
month = {Mon Jul 01 00:00:00 EDT 1996}
}

Conference:
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