 Analysis of the greedy approach in problems of maximum k‐coverageDorit S. Hochbaum and Anu Pathria Naval Research Logistics (NRL), 1998, vol. 45, issue 6, 615-627 Abstract: 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 Date: 1998 Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:wly:navres:v:45:y:1998:i:6:p:615-627 Access Statistics for this article More articles in Naval Research Logistics (NRL) from John Wiley & Sons |
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