### Abstract

The path-distance-width of a graph measures how close the graph is to a path. We consider the problem of determining the path-distance-width for graphs with chain-like structures such as k-cocomparability graphs, AT-free graphs, and interval graphs. We first show that the problem is NP-hard even for a very restricted subclass of AT-free graphs. Next we present simple approximation algorithms with constant approximation ratios for graphs with chain-like structures. For instance, our algorithm for AT-free graphs has approximation factor 3 and runs in linear time. We also show that the problem is solvable in polynomial time for the class of cochain graphs, which is a subclass of the class of proper interval graphs.

Original language | English |
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Title of host publication | Graph-Theoretic Concepts in Computer Science - 37th International Workshop, WG 2011, Revised Papers |

Pages | 271-282 |

Number of pages | 12 |

Volume | 6986 LNCS |

DOIs | |

Publication status | Published - Dec 1 2011 |

Event | 37th International Workshop on Graph-Theoretic Concepts in Computer Science, WG 2011 - Tepla Monastery, Czech Republic Duration: Jun 21 2011 → Jun 24 2011 |

### 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 | 6986 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 37th International Workshop on Graph-Theoretic Concepts in Computer Science, WG 2011 |
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Country | Czech Republic |

City | Tepla Monastery |

Period | 6/21/11 → 6/24/11 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Computer Science(all)
- Theoretical Computer Science

### Cite this

*Graph-Theoretic Concepts in Computer Science - 37th International Workshop, WG 2011, Revised Papers*(Vol. 6986 LNCS, pp. 271-282). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 6986 LNCS). https://doi.org/10.1007/978-3-642-25870-1_25

**Approximability of the path-distance-width for AT-free graphs.** / Otachi, Yota; Saitoh, Toshiki; Yamanaka, Katsuhisa; Kijima, Shuji; Okamoto, Yoshio; Ono, Hirotaka; Uno, Yushi; Yamazaki, Koichi.

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

*Graph-Theoretic Concepts in Computer Science - 37th International Workshop, WG 2011, Revised Papers.*vol. 6986 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 6986 LNCS, pp. 271-282, 37th International Workshop on Graph-Theoretic Concepts in Computer Science, WG 2011, Tepla Monastery, Czech Republic, 6/21/11. https://doi.org/10.1007/978-3-642-25870-1_25

}

TY - GEN

T1 - Approximability of the path-distance-width for AT-free graphs

AU - Otachi, Yota

AU - Saitoh, Toshiki

AU - Yamanaka, Katsuhisa

AU - Kijima, Shuji

AU - Okamoto, Yoshio

AU - Ono, Hirotaka

AU - Uno, Yushi

AU - Yamazaki, Koichi

PY - 2011/12/1

Y1 - 2011/12/1

N2 - The path-distance-width of a graph measures how close the graph is to a path. We consider the problem of determining the path-distance-width for graphs with chain-like structures such as k-cocomparability graphs, AT-free graphs, and interval graphs. We first show that the problem is NP-hard even for a very restricted subclass of AT-free graphs. Next we present simple approximation algorithms with constant approximation ratios for graphs with chain-like structures. For instance, our algorithm for AT-free graphs has approximation factor 3 and runs in linear time. We also show that the problem is solvable in polynomial time for the class of cochain graphs, which is a subclass of the class of proper interval graphs.

AB - The path-distance-width of a graph measures how close the graph is to a path. We consider the problem of determining the path-distance-width for graphs with chain-like structures such as k-cocomparability graphs, AT-free graphs, and interval graphs. We first show that the problem is NP-hard even for a very restricted subclass of AT-free graphs. Next we present simple approximation algorithms with constant approximation ratios for graphs with chain-like structures. For instance, our algorithm for AT-free graphs has approximation factor 3 and runs in linear time. We also show that the problem is solvable in polynomial time for the class of cochain graphs, which is a subclass of the class of proper interval graphs.

UR - http://www.scopus.com/inward/record.url?scp=84855408658&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84855408658&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-25870-1_25

DO - 10.1007/978-3-642-25870-1_25

M3 - Conference contribution

SN - 9783642258695

VL - 6986 LNCS

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

SP - 271

EP - 282

BT - Graph-Theoretic Concepts in Computer Science - 37th International Workshop, WG 2011, Revised Papers

ER -