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

Johan M. M. Van Rooij, Hans L. Bodlaender, Marc Herbstritt
2008 Symposium on Theoretical Aspects of Computer Science  
Design by measure and conquer, a faster exact algorithm for dominating set Citation for published version (APA): van Rooij, J. M. M., & Bodlaender, H. L. (2008). Design by measure and conquer, a faster exact algorithm for dominating set. arXiv. 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. In this paper, we propose to use measure and conquer also as a tool in the design
more » ... 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.
doi:10.4230/lipics.stacs.2008.1329 dblp:conf/stacs/RooijB08 fatcat:q7qc77qdevgwvntf5fufk4akxq