Multicriteria approximation through decomposition
- Carnegie Mellon Univ., Pittsburgh, PA (United States). School of Computer Science
- Univ. of Wuerzburg (Germany). Dept. of Computer Science
- Los Alamos National Lab., NM (United States)
- Sandia National Labs., Albuquerque, NM (United States). Applied Mathematics Dept.
- Rutgers Univ., NJ (United States). Dept. of Computer Science
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 their 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. Their 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 also 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.
- Research Organization:
- Los Alamos National Lab., NM (United States); Sandia National Labs., Albuquerque, NM (United States)
- Sponsoring Organization:
- National Science Foundation, Washington, DC (United States)
- DOE Contract Number:
- W-7405-ENG-36; AC04-94AL85000
- OSTI ID:
- 672075
- Report Number(s):
- LA-UR--97-5198; CONF-980633--; ON: DE98005726
- Country of Publication:
- United States
- Language:
- English
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