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 journalArticle

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 languageEnglish
Pages (from-to)69-77
Number of pages9
JournalDiscrete Applied Mathematics
Volume168
DOIs
Publication statusPublished - May 11 2014

Fingerprint

Approximation algorithms
Computational complexity
Polynomials
Path
Graph in graph theory
Proper Interval Graphs
Class
Graph Classes
Approximation
Linear Time
Approximation Algorithms
Polynomial time
NP-complete problem

All Science Journal Classification (ASJC) codes

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

Cite this

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.

In: Discrete Applied Mathematics, Vol. 168, 11.05.2014, p. 69-77.

Research output: Contribution to journalArticle

Otachi, Yota ; Saitoh, Toshiki ; Yamanaka, Katsuhisa ; Kijima, Shuji ; Okamoto, Yoshio ; Ono, Hirotaka ; Uno, Yushi ; Yamazaki, Koichi. / Approximating the path-distance-width for AT-free graphs and graphs in related classes. In: Discrete Applied Mathematics. 2014 ; Vol. 168. pp. 69-77.
@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 = "5",
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

VL - 168

SP - 69

EP - 77

JO - Discrete Applied Mathematics

JF - Discrete Applied Mathematics

SN - 0166-218X

ER -