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

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. The 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 present an O((H222H1D2H)D1poly(n)) time algorithm, where H is the maximum height of two input trees.

[1]  Atsuhiro Takasu,et al.  Efficient Exponential Time Algorithms for Edit Distance between Unordered Trees , 2012, CPM.

[2]  Erik D. Demaine,et al.  An optimal decomposition algorithm for tree edit distance , 2006, TALG.

[3]  Fabrizio Grandoni,et al.  Resilient dictionaries , 2009, TALG.

[4]  Kaizhong Zhang,et al.  On the Editing Distance Between Unordered Labeled Trees , 1992, Inf. Process. Lett..

[5]  Mikkel Thorup,et al.  An O(n log n) algorithm for the maximum agreement subtree problem for binary trees , 1996, SODA '96.

[6]  Atsuhiro Takasu,et al.  Author's Personal Copy Theoretical Computer Science Approximation and Parameterized Algorithms for Common Subtrees and Edit Distance between Unordered Trees , 2022 .

[7]  Atsuhiro Takasu,et al.  A Clique-Based Method Using Dynamic Programming for Computing Edit Distance Between Unordered Trees , 2012, J. Comput. Biol..

[8]  Atsuhiro Takasu,et al.  On the Complexity of Finding a Largest Common Subtree of Bounded Degree , 2013, FCT.

[9]  Heikki Mannila,et al.  Ordered and Unordered Tree Inclusion , 1995, SIAM J. Comput..

[10]  Mauro Dell'Amico,et al.  The k-cardinality Assignment Problem , 1997, Discret. Appl. Math..

[11]  Tatsuya Akutsu,et al.  KCaM (KEGG Carbohydrate Matcher): a software tool for analyzing the structures of carbohydrate sugar chains , 2004, Nucleic Acids Res..

[12]  Michael R. Fellows,et al.  Parameterized Complexity , 1998 .

[13]  Kuo-Chung Tai,et al.  The Tree-to-Tree Correction Problem , 1979, JACM.

[14]  William E. Higgins,et al.  System for the analysis and visualization of large 3D anatomical trees , 2007, Comput. Biol. Medicine.

[15]  Jörg Flum,et al.  Parameterized Complexity Theory , 2006, Texts in Theoretical Computer Science. An EATCS Series.

[16]  Tiziana Catarci,et al.  Structure-aware XML Object Identification , 2006, IEEE Data Eng. Bull..

[17]  Michal Ziv-Ukelson,et al.  Unrooted unordered homeomorphic subtree alignment of RNA trees , 2013, Algorithms for Molecular Biology.

[18]  Kaizhong Zhang,et al.  Exact and approximate algorithms for unordered tree matching , 1994, IEEE Trans. Syst. Man Cybern..

[19]  Gabriel Valiente,et al.  Algorithms on Trees and Graphs , 2002, Springer Berlin Heidelberg.

[20]  Atsuhiro Takasu,et al.  Exact algorithms for computing the tree edit distance between unordered trees , 2010, Theor. Comput. Sci..

[21]  Tao Jiang,et al.  Some MAX SNP-Hard Results Concerning Unordered Labeled Trees , 1994, Inf. Process. Lett..

[22]  Yair Horesh,et al.  Designing an A* Algorithm for Calculating Edit Distance between Rooted-Unordered Trees , 2006, J. Comput. Biol..

[23]  Kouichi Hirata,et al.  Improved MAX SNP-Hard Results for Finding an Edit Distance between Unordered Trees , 2011, CPM.

[24]  Kai Wang,et al.  A syntactic tree matching approach to finding similar questions in community-based qa services , 2009, SIGIR.

[25]  Erik D. Demaine,et al.  An O(n^3)-Time Algorithm for Tree Edit Distance , 2005, ArXiv.