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

Yota Otachi; Toshiki Saitoh; Katsuhisa Yamanaka; Shuji Kijima; Yoshio Okamoto; Hirotaka Ono; Yushi Uno; Koichi Yamazaki

doi:10.1016/j.dam.2012.11.015

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

Yota Otachi, Toshiki Saitoh, Katsuhisa Yamanaka, Shuji Kijima, Yoshio Okamoto, Hirotaka Ono, Yushi Uno, Koichi Yamazaki

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

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	https://doi.org/10.1016/j.dam.2012.11.015
Publication status	Published - May 11 2014

All Science Journal Classification (ASJC) codes

Discrete Mathematics and Combinatorics
Applied Mathematics

Access to Document

10.1016/j.dam.2012.11.015

Cite this

@article{8a6667cab3e94288b35abf33e3062bb7,

title = "Approximating the path-distance-width for AT-free graphs and graphs in related classes",

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.",

author = "Yota Otachi and Toshiki Saitoh and Katsuhisa Yamanaka and Shuji Kijima and Yoshio Okamoto and Hirotaka Ono and Yushi Uno and Koichi Yamazaki",

year = "2014",

month = may,

day = "11",

doi = "10.1016/j.dam.2012.11.015",

language = "English",

volume = "168",

pages = "69--77",

journal = "Discrete Applied Mathematics",

issn = "0166-218X",

publisher = "Elsevier",

}

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

SN - 0166-218X

VL - 168

SP - 69

EP - 77

JO - Discrete Applied Mathematics

JF - Discrete Applied Mathematics

ER -

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

Abstract

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this