Exact algorithms for dominating set |
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Authors: | Johan MM van Rooij Hans L Bodlaender |
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Institution: | Department of Information and Computing Sciences, Utrecht University, P.O. Box 80.089, 3508 TB Utrecht, The Netherlands |
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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 O(1.4969n) time and polynomial space algorithm. |
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Keywords: | Exact algorithms Exponential time algorithms Branch and reduce Measure and conquer Dominating set Computer aided algorithm design |
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