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

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 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:

• Type: Journal
• Year: 2008
• Where: CORR
• Authors: Johan M. M. van Rooij, Hans L. Bodlaender
• Keywords: Algorithms, CORR 2008, Dominating Set, Education, Exact Algorithms