• DOI:10.1002/(SICI)1520-6750(199809)45:6<615::AID-NAV5>3.0.CO;2-5
• Corpus ID: 12921897

Analysis of the greedy approach in problems of maximum k‐coverage

@article{Hochbaum1998AnalysisOT,
  title={Analysis of the greedy approach in problems of maximum k‐coverage},
  author={Dorit S. Hochbaum and Anu Pathria},
  journal={Naval Research Logistics},
  year={1998},
  volume={45},
  pages={615-627}
}

• D. Hochbaum, A. Pathria
• Published 1 September 1998
• Mathematics
• Naval Research Logistics

In this paper, we consider a general covering problem in which k subsets are to be selected such that their union covers as large a weight of objects from a universal set of elements as possible. Each subset selected must satisfy some structural constraints. We analyze the quality of a k-stage covering algorithm that relies, at each stage, on greedily selecting a subset that gives maximum improvement in terms of overall coverage. We show that such greedily constructed solutions are guaranteed to be within a factor of 1 − 1/e of the optimal solution. In some cases, selecting a best solution at each stage may itself be difficult; we show that if a β-approximate best solution is chosen at each stage, then the overall solution constructed is guaranteed to be within a factor of 1 − 1/eβ of the optimal. Our results also yield a simple proof that the number of subsets used by the greedy approach to achieve entire coverage of the universal set is within a logarithmic factor of the optimal number of subsets. Examples of problems that fall into the family of general covering problems considered, and for which the algorithmic results apply, are discussed. © 1998 John Wiley & Sons, Inc. Naval Research Logistics 45: 615–627, 1998