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

Authors:
Yota Otachi;Toshiki Saitoh;Katsuhisa Yamanaka;Shuji Kijima;Yoshio Okamoto;Hirotaka Ono;Yushi Uno;Koichi Yamazaki
Affiliations:
School of Information Science, Japan Advanced Institute of Science and Technology, Ishikawa, 923-1292, Japan;Graduate School of Engineering, Kobe University, Kobe, 657-8501, Japan;Department of Electrical Engineering and Computer Science, Iwate University, Iwate 020-8550, Japan;Graduate School of Information Science and Electrical Engineering, Kyushu University, Fukuoka, 819-0395, Japan;Department of Communication Engineering and Informatics, Graduate School of Informatics and Engineering, University of Electro-Communications, Chofugaoka 1-5-1, Chofu, Tokyo, 182-8585, Japan;Department of Economic Engineering, Kyushu University, 6-19-1 Hakozaki Higashi-ku, Fukuoka 812-8581, Japan;Department of Mathematics and Information Sciences, Graduate School of Science, Osaka Prefecture University, 1-1 Gakuen-cho, Naka-ku, Sakai 599-8531, Japan;Department of Computer Science, Gunma University, 1-5-1 Tenjin-cho, Kiryu, Gunma, 376-8515, Japan
Venue:
Discrete Applied Mathematics
Year:
2014

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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.