### 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) |
---|---|

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 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)

### 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

}

*Combinatorial Algorithms - 27th International Workshop, IWOCA 2016, Proceedings.*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 9843 LNCS, Springer Verlag, pp. 385-396, 27th International Workshop on Combinatorial Algorithms, IWOCA 2016, Helsinki, Finland, 8/17/16. https://doi.org/10.1007/978-3-319-44543-4_30

**Faster computation of path-width.** / Furer, Martin.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

TY - GEN

T1 - Faster computation of path-width

AU - Furer, Martin

PY - 2016/1/1

Y1 - 2016/1/1

N2 - 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 k3 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(k2)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.

AB - 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 k3 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(k2)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.

UR - http://www.scopus.com/inward/record.url?scp=84984870423&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84984870423&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-44543-4_30

DO - 10.1007/978-3-319-44543-4_30

M3 - Conference contribution

SN - 9783319445427

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 385

EP - 396

BT - Combinatorial Algorithms - 27th International Workshop, IWOCA 2016, Proceedings

A2 - Mäkinen, Veli

A2 - Puglisi, Simon J.

A2 - Salmela, Leena

PB - Springer Verlag

ER -