Set Cover Problem
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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. The set covering problem is a classical question in computer science and complexity theory. It is a problem "whose study has led to the development of fundamental techniques for the entire field" of approximation algorithms. The decision version of set covering is NP-complete, and the optimization version of set cover is NP-hard. In computer science and operations research, approximation algorithms are algorithms used to find approximate solutions to optimization prob...
Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. The set covering problem is a classical question in computer science and complexity theory. It is a problem "whose study has led to the development of fundamental techniques for the entire field" of approximation algorithms. The decision version of set covering is NP-complete, and the optimization version of set cover is NP-hard. In computer science and operations research, approximation algorithms are algorithms used to find approximate solutions to optimization problems. Approximation algorithms are often associated with NP-hard problems; since it is unlikely that there can ever be efficient polynomial time exact algorithms solving NP-hard problems, one settles for polynomial time sub-optimal solutions. Unlike heuristics, which usually only find reasonably good solutions reasonably fast, one wants provable solution quality and provable run time bounds.Ideally, the approximation is optimal up to a small constant factor (for instance within 5% of the optimal solution). Approximation algorithms are increasingly being used for problems where exact polynomial-time algorithms are known but are too expensive due to the input size.
