Design by Measure and Conquer, A Faster Exact Algorithm for Dominating Set

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dc.creatorVan Rooij, Johan M. M.
dc.creatorBodlaender, Hans L.
dc.date2008-02-20
dc.date.accessioned2026-07-07T09:21:59Z
dc.date.available2026-07-07T09:21:59Z
dc.descriptionThe measure and conquer approach has proven to be a powerful tool to analyse exact algorithms for combinatorial problems, like Dominating Set and Independent Set. In this paper, we propose to use measure and conquer also as a tool in the design of algorithms. In an iterative process, we can obtain a series of branch and reduce algorithms. A mathematical analysis of an algorithm in the series with measure and conquer results in a quasiconvex programming problem. The solution by computer to this problem not only gives a bound on the running time, but also can give a new reduction rule, thus giving a new, possibly faster algorithm. This makes design by measure and conquer a form of computer aided algorithm design. When we apply the methodology to a Set Cover modelling of the Dominating Set problem, we obtain the currently fastest known exact algorithms for Dominating Set: an algorithm that uses $O(1.5134^n)$ time and polynomial space, and an algorithm that uses $O(1.5063^n)$ time.
dc.identifierhttps://arxiv.org/abs/0802.2827
dc.identifierhttp://arxiv.org/abs/0802.2827
dc.identifierDans Proceedings of the 25th Annual Symposium on the Theoretical Aspects of Computer Science - STACS 2008, Bordeaux : France (2008)
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/155220
dc.subjectData Structures and Algorithms
dc.titleDesign by Measure and Conquer, A Faster Exact Algorithm for Dominating Set
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