### Abstract

Tree-width and path-width are widely successful concepts.Many NP-hard problems have efficient solutions when restricted to graphs of bounded tree-width.Many efficient algorithms are based on a tree decomposition.Sometimes the more restricted path decomposition is required.The bottleneck for such algorithms is often the computation of the width and a corresponding tree or path decomposition.For graphs with n vertices and tree-width or path-width k, the standard linear time algorithm to compute these decompositions dates back to 1996.Its running time is linear in n and exponential in k^{3} and not usable in practice.Here we present a more efficient algorithm to compute the path-width and provide a path decomposition.Its running time is 2O(k^{2})n.In the classical algorithm of Bodlaender and Kloks, the path decomposition is computed from a tree decomposition.Here, an optimal path decomposition is computed from a path decomposition of about twice the width.The latter is computed from a constant factor smaller graph.

Original language | English (US) |
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Title of host publication | Combinatorial Algorithms - 27th International Workshop, IWOCA 2016, Proceedings |

Editors | Veli Mäkinen, Simon J. Puglisi, Leena Salmela |

Publisher | Springer Verlag |

Pages | 385-396 |

Number of pages | 12 |

ISBN (Print) | 9783319445427 |

DOIs | |

State | Published - Jan 1 2016 |

Event | 27th International Workshop on Combinatorial Algorithms, IWOCA 2016 - Helsinki, Finland Duration: Aug 17 2016 → Aug 19 2016 |

### 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 | 9843 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 27th International Workshop on Combinatorial Algorithms, IWOCA 2016 |
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Country | Finland |

City | Helsinki |

Period | 8/17/16 → 8/19/16 |

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)

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## Cite this

*Combinatorial Algorithms - 27th International Workshop, IWOCA 2016, Proceedings*(pp. 385-396). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9843 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-319-44543-4_30