### Abstract

We consider the problem of determining the path-distance-width for AT-free graphs and graphs in related classes such as k-cocomparability graphs, proper interval graphs, cobipartite graphs, and cochain graphs. We first show that the problem is NP-hard even for cobipartite graphs, and thus for AT-free graphs. Next we present simple approximation algorithms with constant approximation ratios for AT-free graphs and graphs in the related graph classes mentioned above. 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 cochain graphs, which form a subclass of the class of proper interval graphs.

Original language | English |
---|---|

Pages (from-to) | 69-77 |

Number of pages | 9 |

Journal | Discrete Applied Mathematics |

Volume | 168 |

DOIs | |

Publication status | Published - May 11 2014 |

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### All Science Journal Classification (ASJC) codes

- Discrete Mathematics and Combinatorics
- Applied Mathematics

### Cite this

*Discrete Applied Mathematics*,

*168*, 69-77. https://doi.org/10.1016/j.dam.2012.11.015

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

Research output: Contribution to journal › Article

*Discrete Applied Mathematics*, vol. 168, pp. 69-77. https://doi.org/10.1016/j.dam.2012.11.015

}

TY - JOUR

T1 - Approximating the path-distance-width for AT-free graphs and graphs in related classes

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 - 2014/5/11

Y1 - 2014/5/11

N2 - We consider the problem of determining the path-distance-width for AT-free graphs and graphs in related classes such as k-cocomparability graphs, proper interval graphs, cobipartite graphs, and cochain graphs. We first show that the problem is NP-hard even for cobipartite graphs, and thus for AT-free graphs. Next we present simple approximation algorithms with constant approximation ratios for AT-free graphs and graphs in the related graph classes mentioned above. 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 cochain graphs, which form a subclass of the class of proper interval graphs.

AB - We consider the problem of determining the path-distance-width for AT-free graphs and graphs in related classes such as k-cocomparability graphs, proper interval graphs, cobipartite graphs, and cochain graphs. We first show that the problem is NP-hard even for cobipartite graphs, and thus for AT-free graphs. Next we present simple approximation algorithms with constant approximation ratios for AT-free graphs and graphs in the related graph classes mentioned above. 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 cochain graphs, which form a subclass of the class of proper interval graphs.

UR - http://www.scopus.com/inward/record.url?scp=84894638703&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84894638703&partnerID=8YFLogxK

U2 - 10.1016/j.dam.2012.11.015

DO - 10.1016/j.dam.2012.11.015

M3 - Article

AN - SCOPUS:84894638703

VL - 168

SP - 69

EP - 77

JO - Discrete Applied Mathematics

JF - Discrete Applied Mathematics

SN - 0166-218X

ER -