On Combinatorial Approximation of Covering 0-1 Integer Programs and Partial Set Cover

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• 作者：Toshihiro Fujito
• 关键词：combinatorial optimization ; approximation algorithm ; covering integer program ; partial cover
• 刊名：Journal of Combinatorial Optimization
• 出版年：2004
• 出版时间：December 2004
• 年：2004
• 卷：8
• 期：4
• 页码：439-452
• 全文大小：150 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Combinatorics
  Convex and Discrete Geometry
  Mathematical Modeling and IndustrialMathematics
  Theory of Computation
  Optimization
  Operation Research and Decision Theory
  
• 出版者：Springer Netherlands
• ISSN：1573-2886

文摘

The problems dealt with in this paper are generalizations of the set cover problem, min{cx | Ax b, x {0,1}n}, where c Q₊n, A {0,1}m × n, b 1. The covering 0-1 integer program is the one, in this formulation, with arbitrary nonnegative entries of A and b, while the partial set cover problem requires only m–K constrains (or more) in Ax b to be satisfied when integer K is additionall specified. While many approximation algorithms have been recently developed for these problems and their special cases, using computationally rather expensive (albeit polynomial) LP-rounding (or SDP-rounding), we present a more efficient purely combinatorial algorithm and investigate its approximation capability for them. It will be shown that, when compared with the best performance known today and obtained by rounding methods, although its performance comes short in some special cases, it is at least equally good in general, extends for partial vertex cover, and improves for weighted multicover, partial set cover, and further generalizations.