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

Research output: Chapter in Book/Report/Conference proceedingConference contribution

2 Citations (Scopus)

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.

Original languageEnglish
Title of host publicationGraph-Theoretic Concepts in Computer Science - 37th International Workshop, WG 2011, Revised Papers
Pages271-282
Number of pages12
Volume6986 LNCS
DOIs
Publication statusPublished - Dec 1 2011
Event37th International Workshop on Graph-Theoretic Concepts in Computer Science, WG 2011 - Tepla Monastery, Czech Republic
Duration: Jun 21 2011Jun 24 2011

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume6986 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other37th International Workshop on Graph-Theoretic Concepts in Computer Science, WG 2011
CountryCzech Republic
CityTepla Monastery
Period6/21/116/24/11

Fingerprint

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

All Science Journal Classification (ASJC) codes

  • Computer Science(all)
  • Theoretical Computer Science

Cite this

Otachi, Y., Saitoh, T., Yamanaka, K., Kijima, S., Okamoto, Y., Ono, H., ... Yamazaki, K. (2011). Approximability of the path-distance-width for AT-free graphs. In Graph-Theoretic Concepts in Computer Science - 37th International Workshop, WG 2011, Revised Papers (Vol. 6986 LNCS, pp. 271-282). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 6986 LNCS). https://doi.org/10.1007/978-3-642-25870-1_25

Approximability of the path-distance-width for AT-free graphs. / Otachi, Yota; Saitoh, Toshiki; Yamanaka, Katsuhisa; Kijima, Shuji; Okamoto, Yoshio; Ono, Hirotaka; Uno, Yushi; Yamazaki, Koichi.

Graph-Theoretic Concepts in Computer Science - 37th International Workshop, WG 2011, Revised Papers. Vol. 6986 LNCS 2011. p. 271-282 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 6986 LNCS).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Otachi, Y, Saitoh, T, Yamanaka, K, Kijima, S, Okamoto, Y, Ono, H, Uno, Y & Yamazaki, K 2011, Approximability of the path-distance-width for AT-free graphs. in Graph-Theoretic Concepts in Computer Science - 37th International Workshop, WG 2011, Revised Papers. vol. 6986 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 6986 LNCS, pp. 271-282, 37th International Workshop on Graph-Theoretic Concepts in Computer Science, WG 2011, Tepla Monastery, Czech Republic, 6/21/11. https://doi.org/10.1007/978-3-642-25870-1_25
Otachi Y, Saitoh T, Yamanaka K, Kijima S, Okamoto Y, Ono H et al. Approximability of the path-distance-width for AT-free graphs. In Graph-Theoretic Concepts in Computer Science - 37th International Workshop, WG 2011, Revised Papers. Vol. 6986 LNCS. 2011. p. 271-282. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-642-25870-1_25
Otachi, Yota ; Saitoh, Toshiki ; Yamanaka, Katsuhisa ; Kijima, Shuji ; Okamoto, Yoshio ; Ono, Hirotaka ; Uno, Yushi ; Yamazaki, Koichi. / Approximability of the path-distance-width for AT-free graphs. Graph-Theoretic Concepts in Computer Science - 37th International Workshop, WG 2011, Revised Papers. Vol. 6986 LNCS 2011. pp. 271-282 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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