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}
}
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… 

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References

SHOWING 1-10 OF 26 REFERENCES
Approximation Algorithms for the k-Clique Covering Problem
TLDR
This paper provides a collection of approximation algorithms for various clique sizes with proven worst-case bounds, and shows that these special classes of set covering problems can be solved with better worst- case bounds and/or complexity than if treated as general set coveringblems.
A Greedy Heuristic for the Set-Covering Problem
TLDR
It turns out that the ratio between the two grows at most logarithmically in the largest column sum of A when all the components of cT are the same, which reduces to a theorem established previously by Johnson and Lovasz.
Approximation Algorithms for Combinatorial Problems
Approximation algorithms for NP-complete problems on planar graphs
  • B. Baker
  • Mathematics, Computer Science
    24th Annual Symposium on Foundations of Computer Science (sfcs 1983)
  • 1983
TLDR
A general technique that can be used to obtain approximation algorithms for various NP-complete problems on planar graphs, which includes maximum independent set, maximum tile salvage, partition into triangles, maximum H-matching, minimum vertex cover, minimum dominating set, and minimum edge dominating set.
The Maximum Coverage Location Problem
In this paper we define and discuss the following problem which we call the maximum coverage location problem. A transportation network is given together with the locations of customers and
On the k-layer planar subset and via minimization problems
  • J. Cong, C. Liu
  • Computer Science
    Proceedings of the European Design Automation Conference, 1990., EDAC.
  • 1990
TLDR
It can be shown that under a realistic assumption, all the channels for inter-block connections in the general cell design style are crossing channels and the authors algorithms are based on an efficient algorithm for computing a maximum weighted.
The Minimal Cut Cover of a Graph
We consider a problem which occurs in testing for short circuits in printed circuit board components. This problem can be modeled as the covering of the edges of an undirected graph by cuts. In
Improved approximation algorithms for maximum cut and satisfiability problems using semidefinite programming
TLDR
This algorithm gives the first substantial progress in approximating MAX CUT in nearly twenty years, and represents the first use of semidefinite programming in the design of approximation algorithms.
Approximation schemes for covering and packing problems in image processing and VLSI
TLDR
The unified technique that is introduced here, referred to as the shifting strategy, is applicable to numerous geometric covering and packing problems and how it varies with problem parameters is illustrated.
Approximation Algorithms for NP-Hard Problems
TLDR
This book introduces unifying techniques in the analysis of approximation algorithms, intended for computer scientists and operations researchers interested in specific algorithm implementations, as well as design tools for algorithms.
...
1
2
3
...