## On exact algorithms for treewidth

Please always quote using this URN: urn:nbn:de:0297-zib-9265

- We give experimental and theoretical results on the problem of computing the treewidth of a graph by exact exponential time algorithms using exponential space or using only polynomial space. We first report on an implementation of a dynamic programming algorithm for computing the treewidth of a graph with running time $O^\ast(2^n)$. This algorithm is based on the old dynamic programming method introduced by Held and Karp for the {\sc Tra veling Salesman} problem. We use some optimizations that do not affect the worst case running time but improve on the running time on actual instances and can be seen to be practical for small instances. However, our experiments show that the space use d by the algorithm is an important factor to what input sizes the algorithm is effective. For this purpose, we settle the problem of computing treewidth under the restriction that the space used is only polynomial. In this direction we give a simple $O^\ast(4^n)$ al gorithm that requires {\em polynomial} space. We also show that with a more complicated algorithm, using balanced separators, {\sc Treewidth} can be computed in $O^\ast(2.9512^n)$ time and polynomial space.

Author: | Hans L. Bodlaender, Fedor V. Fomin, Arie M.C.A. Koster, Dieter Kratsch, Dimitrios M. Thilikos |
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Document Type: | ZIB-Report |

Tag: | exponential algorithms; treewidth |

MSC-Classification: | 05-XX COMBINATORICS (For finite fields, see 11Txx) / 05Cxx Graph theory (For applications of graphs, see 68R10, 81Q30, 81T15, 82B20, 82C20, 90C35, 92E10, 94C15) / 05C85 Graph algorithms [See also 68R10, 68W05] |

68-XX COMPUTER SCIENCE (For papers involving machine computations and programs in a specific mathematical area, see Section -04 in that area) / 68Rxx Discrete mathematics in relation to computer science / 68R10 Graph theory (including graph drawing) [See also 05Cxx, 90B10, 90B35, 90C35] | |

Date of first Publication: | 2006/06/16 |

Series (Serial Number): | ZIB-Report (06-32) |

ZIB-Reportnumber: | 06-32 |

Published in: | An extended abstract appeared in: Proceedings 14th Annual European Symposium on Algorithms, ESA 2006, Lecture Notes in Computer Science, Vol. 4168, 2006, pp. 672-683 |