Approximability of the path-distance-width for AT-free graphs

  • Authors:

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

  • Affiliations:

  • Graduate School of Information Sciences, Tohoku University, JSPS, Sendai, Japan;Erato Minato Discrete Structure Manipulation System Project, Japan Science and Technology Agency, Sapporo, Hokkaido, Japan;Department of Electrical Engineering and Computer Science, Iwate University, Morioka, Iwate, Japan;Graduate School of Information Science and Electrical Engineering, Kyushu University, Fukuoka, Japan;Center for Graduate Education Initiative, JAIST, Nomi, Ishikawa, Japan;Department of Economic Engineering, Kyushu University, Higashi-ku, Fukuoka, Japan;Department of Mathematics and Information Sciences, Graduate School of Science, Osaka Prefecture University, Naka-ku, Sakai, Japan;Department of Computer Science, Gunma University, Kiryu, Gunma, Japan

  • Venue:
  • WG'11 Proceedings of the 37th international conference on Graph-Theoretic Concepts in Computer Science
  • Year:
  • 2011

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Abstract

The path-distance-width of a graph measures how close the graph is to a path. We consider the problem of determining the path-distance-width for graphs with chain-like structures such as k-cocomparability graphs, AT-free graphs, and interval graphs. We first show that the problem is NP-hard even for a very restricted subclass of AT-free graphs. Next we present simple approximation algorithms with constant approximation ratios for graphs with chain-like structures. 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 the class of cochain graphs, which is a subclass of the class of proper interval graphs.