### 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 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.

Original language | English |
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Journal | arXiv |

Publication status | Published - 20 Feb 2008 |

Externally published | Yes |

### Keywords

- cs.DS

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## Cite this

van Rooij, J. M. M., & Bodlaender, H. L. (2008). Design by measure and conquer, a faster exact algorithm for dominating set.

*arXiv*.