Bicriteria network design problems
- Los Alamos National Lab., NM (United States)
- Princeton Univ., NJ (United States)
- Massachusetts Inst. of Tech., Cambridge, MA (United States)
- State Univ. of New York, Albany, NY (United States). Dept. of Computer Science
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.
- Research Organization:
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
- Sponsoring Organization:
- USDOE, Washington, DC (United States); National Science Foundation, Washington, DC (United States); Defense Advanced Research Projects Agency, Arlington, VA (United States)
- DOE Contract Number:
- W-7405-ENG-36
- OSTI ID:
- 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
- Resource Relation:
- Other Information: PBD: 20 Nov 1997
- Country of Publication:
- United States
- Language:
- English
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