1. Exact algorithms for dominating set
- Author
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van Rooij, Johan M.M. and Bodlaender, Hans L.
- Subjects
- *
DOMINATING set , *COMPUTER-aided design , *ALGORITHMS , *MATHEMATICAL proofs , *COMBINATORICS , *SET theory , *MATHEMATICAL analysis , *POLYNOMIALS - Abstract
Abstract: The measure and conquer approach has proven to be a powerful tool to analyse exact algorithms for combinatorial problems like Dominating Set and Independent Set. This approach is used in this paper to obtain a faster exact algorithm for Dominating Set. We obtain this algorithm by considering a series of branch and reduce algorithms. This series is the result of an iterative process in which a mathematical analysis of an algorithm in the series with measure and conquer results in a convex or quasiconvex programming problem. The solution, by means of a computer, to this problem not only gives a bound on the running time of the algorithm, but can also give an indication on where to look for a new reduction rule, often giving a new, possibly faster algorithm. As a result, we obtain an time and polynomial space algorithm. [Copyright &y& Elsevier]
- Published
- 2011
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