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 ...
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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(1.4969(n)) time and polynomial space algorithm. (C) 2011 Elsevier B.V. All rights reserved.
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