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

N1 - Copyright:
Copyright 2014 Elsevier B.V., All rights reserved.

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 -