Approximation and parameterized algorithms for common subtrees and edit distance between unordered trees
Given two rooted, labeled, unordered trees, the common subtree problem is to find a bijective matching between subsets of nodes of the trees of maximum cardinality which preserves labels and ancestry relationship. The tree edit distance problem is to determine the least cost sequence of insertions,...
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| Veröffentlicht in: | Theoretical computer science Jg. 470; S. 10 - 22 |
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| Abstract | Given two rooted, labeled, unordered trees, the common subtree problem is to find a bijective matching between subsets of nodes of the trees of maximum cardinality which preserves labels and ancestry relationship. The tree edit distance problem is to determine the least cost sequence of insertions, deletions and substitutions that converts a tree into another given tree. Both problems are known to be hard to approximate within some constant factor in general.
We tackle these problems from two perspectives: giving exact algorithms, either for special cases or in terms of some parameters; and approximation algorithms and hardness of approximation. We present a parameterized algorithm in terms of the number of branching nodes that solves both problems and yields polynomial algorithms for several special classes of trees. This is complemented with a tighter APX-hardness proof that holds when the trees are of height one and two, respectively. Furthermore, we present the first approximation algorithms for both problems. In particular, for the common subtree problem for t trees, we present an algorithm achieving a tlog2(bOPT+1) ratio, where bOPT is the number of branching nodes in the optimal solution. We also present constant factor approximation algorithms for both problems in the case of bounded height trees. |
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| AbstractList | Given two rooted, labeled, unordered trees, the common subtree problem is to find a bijective matching between subsets of nodes of the trees of maximum cardinality which preserves labels and ancestry relationship. The tree edit distance problem is to determine the least cost sequence of insertions, deletions and substitutions that converts a tree into another given tree. Both problems are known to be hard to approximate within some constant factor in general.
We tackle these problems from two perspectives: giving exact algorithms, either for special cases or in terms of some parameters; and approximation algorithms and hardness of approximation. We present a parameterized algorithm in terms of the number of branching nodes that solves both problems and yields polynomial algorithms for several special classes of trees. This is complemented with a tighter APX-hardness proof that holds when the trees are of height one and two, respectively. Furthermore, we present the first approximation algorithms for both problems. In particular, for the common subtree problem for t trees, we present an algorithm achieving a tlog2(bOPT+1) ratio, where bOPT is the number of branching nodes in the optimal solution. We also present constant factor approximation algorithms for both problems in the case of bounded height trees. |
| Author | Akutsu, Tatsuya Halldórsson, Magnús M. Tanaka, Keisuke Takasu, Atsuhiro Fukagawa, Daiji |
| Author_xml | – sequence: 1 givenname: Tatsuya surname: Akutsu fullname: Akutsu, Tatsuya email: takutsu@kuicr.kyoto-u.ac.jp organization: Bioinformatics Center, Institute for Chemical Research, Kyoto University, Uji, Kyoto 611-0011, Japan – sequence: 2 givenname: Daiji surname: Fukagawa fullname: Fukagawa, Daiji email: dfukagaw@mail.doshisha.ac.jp organization: Faculty of Culture and Information Science, Doshisha University, Kyoto 610-0394, Japan – sequence: 3 givenname: Magnús M. surname: Halldórsson fullname: Halldórsson, Magnús M. email: mmh@ru.is organization: ICE-TCS, School of Computer Science, Reykjavik University, 101 Reykjavik, Iceland – sequence: 4 givenname: Atsuhiro surname: Takasu fullname: Takasu, Atsuhiro email: takasu@nii.ac.jp organization: National Institute of Informatics, Tokyo 101-8430, Japan – sequence: 5 givenname: Keisuke surname: Tanaka fullname: Tanaka, Keisuke email: keisuke@is.titech.ac.jp organization: Department of Mathematical and Computing Sciences, Tokyo Institute of Technology, Tokyo, Japan |
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| Cites_doi | 10.1016/j.tcs.2004.12.030 10.1089/cmb.2006.13.1165 10.1016/0020-0190(94)90062-0 10.1137/S0097539791218202 10.1016/S0304-3975(97)00278-8 10.1145/322139.322143 10.1007/s00453-008-9213-z 10.1093/nar/gkh473 10.1137/S0097539703437843 10.1145/1644015.1644017 10.1016/0304-3975(95)80029-9 10.1109/21.286387 10.1016/j.compbiomed.2007.06.005 10.1016/0020-0190(92)90136-J 10.1016/j.ipl.2008.09.025 10.1016/j.tcs.2010.10.002 10.1007/BF01202286 10.1007/BF01975866 |
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| Keywords | Approximation algorithms Tree edit distance Parameterized algorithms Dynamic programming Unordered trees |
| Language | English |
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| SubjectTerms | Approximation algorithms Dynamic programming Parameterized algorithms Tree edit distance Unordered trees |
| Title | Approximation and parameterized algorithms for common subtrees and edit distance between unordered trees |
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