TY - GEN

T1 - Approximability of the path-distance-width for AT-free graphs

AU - Otachi, Yota

AU - Saitoh, Toshiki

AU - Yamanaka, Katsuhisa

AU - Kijima, Shuji

AU - Okamoto, Yoshio

AU - Ono, Hirotaka

AU - Uno, Yushi

AU - Yamazaki, Koichi

PY - 2011

Y1 - 2011

N2 - 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.

AB - 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.

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U2 - 10.1007/978-3-642-25870-1_25

DO - 10.1007/978-3-642-25870-1_25

M3 - Conference contribution

AN - SCOPUS:84855408658

SN - 9783642258695

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 271

EP - 282

BT - Graph-Theoretic Concepts in Computer Science - 37th International Workshop, WG 2011, Revised Papers

T2 - 37th International Workshop on Graph-Theoretic Concepts in Computer Science, WG 2011

Y2 - 21 June 2011 through 24 June 2011

ER -