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Approximability of the Path-Distance-Width for AT-free Graphs

  • Yota Otachi
  • Toshiki Saitoh
  • Katsuhisa Yamanaka
  • Shuji Kijima
  • Yoshio Okamoto
  • Hirotaka Ono
  • Yushi Uno
  • Koichi Yamazaki
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6986)

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.

Keywords

Bipartite Graph Linear Time Approximation Ratio Interval Graph Graph Class 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Yota Otachi
    • 1
  • Toshiki Saitoh
    • 2
  • Katsuhisa Yamanaka
    • 3
  • Shuji Kijima
    • 4
  • Yoshio Okamoto
    • 5
  • Hirotaka Ono
    • 6
  • Yushi Uno
    • 7
  • Koichi Yamazaki
    • 8
  1. 1.Graduate School of Information SciencesTohoku University, JSPSSendaiJapan
  2. 2.Erato Minato Discrete Structure Manipulation System ProjectJapan Science and Technology AgencySapporoJapan
  3. 3.Department of Electrical Engineering and Computer ScienceIwate UniversityMoriokaJapan
  4. 4.Graduate School of Information Science and Electrical EngineeringKyushu UniversityFukuokaJapan
  5. 5.Center for Graduate Education InitiativeJAISTNomiJapan
  6. 6.Department of Economic EngineeringKyushu UniversityHigashi-kuJapan
  7. 7.Department of Mathematics and Information Sciences, Graduate School of ScienceOsaka Prefecture UniversityNaka-kuJapan
  8. 8.Department of Computer ScienceGunma UniversityKiryuJapan

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