### Abstract

We develop practically efficient algorithms for computing the treewidth (formula presented) of a graph G. The core of our approach is a new dynamic programming algorithm which, given a graph G, a positive integer k, and a set (formula presented) of minimal separators of G, decides if G has a tree-decomposition of width at most k of a certain canonical form that uses minimal separators only from in the sense that the intersection of every pair of adjacent bags belongs to. This algorithm is used to show a lower bound of (formula presented), setting to be the set of all minimal separators of cardinality at most k and to show an upper bound of k on (formula presented) to be some, hopefully rich, set of such minimal separators. Combining this algorithm with new algorithms for exact and heuristic listing of minimal separators, we obtain exact algorithms for treewidth which overwhelmingly outperform previously implemented algorithms.

Original language | English |
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Title of host publication | Analysis of Experimental Algorithms - Special Event,SEA² 2019, Revised Selected Papers |

Editors | Ilias Kotsireas, Panos Pardalos, Arsenis Tsokas, Konstantinos E. Parsopoulos, Dimitris Souravlias |

Publisher | Springer |

Pages | 219-236 |

Number of pages | 18 |

ISBN (Print) | 9783030340285 |

DOIs | |

Publication status | Published - 1 Jan 2019 |

Event | Special Event on Analysis of Experimental Algorithms, SEA² 2019 - Kalamata, Greece Duration: 24 Jun 2019 → 29 Jun 2019 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 11544 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | Special Event on Analysis of Experimental Algorithms, SEA² 2019 |
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Country | Greece |

City | Kalamata |

Period | 24/06/19 → 29/06/19 |

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## Cite this

*Analysis of Experimental Algorithms - Special Event,SEA² 2019, Revised Selected Papers*(pp. 219-236). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 11544 LNCS). Springer. https://doi.org/10.1007/978-3-030-34029-2_15