TY - GEN

T1 - On the complexity of finding a largest common subtree of bounded degree

AU - Akutsu, Tatsuya

AU - Tamura, Takeyuki

AU - Melkman, Avraham A.

AU - Takasu, Atsuhiro

N1 - Funding Information:
We would like to thank Yefim Dinitz for helpful comments. This work was partially supported by the Collaborative Research Programs of National Institute of Informatics . T.A. and T.T. were partially supported by JSPS , Japan: Grant-in-Aid 26240034 and Grant-in-Aid 25730005 , respectively.

PY - 2013/9/3

Y1 - 2013/9/3

N2 - The largest common subtree problem is to find a bijective mapping between subsets of nodes of two input rooted trees of maximum cardinality or weight that preserves labels and ancestry relationship. This problem is known to be NP-hard for unordered trees. In this paper, we consider a restricted unordered case in which the maximum outdegree of a common subtree is bounded by a constant D. We present an O(nD) time algorithm where n is the maximum size of two input trees, which improves a previous O(n2D) time algorithm. We also prove that this restricted problem is W[1]-hard for parameter D.

AB - The largest common subtree problem is to find a bijective mapping between subsets of nodes of two input rooted trees of maximum cardinality or weight that preserves labels and ancestry relationship. This problem is known to be NP-hard for unordered trees. In this paper, we consider a restricted unordered case in which the maximum outdegree of a common subtree is bounded by a constant D. We present an O(nD) time algorithm where n is the maximum size of two input trees, which improves a previous O(n2D) time algorithm. We also prove that this restricted problem is W[1]-hard for parameter D.

KW - dynamic programming

KW - parameterized complexity

KW - tree edit distance

KW - unordered trees

UR - http://www.scopus.com/inward/record.url?scp=84883196403&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-40164-0_4

DO - 10.1007/978-3-642-40164-0_4

M3 - Conference contribution

AN - SCOPUS:84883196403

SN - 9783642401633

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

SP - 4

EP - 15

BT - Fundamentals of Computation Theory - 19th International Symposium, FCT 2013, Proceedings

T2 - 19th International Symposium on Fundamentals of Computation Theory, FCT 2013

Y2 - 19 August 2013 through 21 August 2013

ER -