Paper Info
Title
Approximation and parameterized algorithms for common subtrees and edit distance between unordered trees
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 tlog"2(b"O"P"T+1) ratio, where b"O"P"T 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.
Year
DOI
Venue
2013
10.1016/j.tcs.2012.11.017
Theor. Comput. Sci.
Keywords
DocType
Volume
parameterized algorithm,constant factor,special case,common subtree problem,bounded height tree,common subtrees,present constant factor approximation,approximation algorithm,unordered tree,exact algorithm,distance problem
Journal
470,
ISSN
Citations 
PageRank 
0304-3975
8
0.54
References 
Authors
19
5
Name
Order
Citations
PageRank
Tatsuya Akutsu12169216.05
Daiji Fukagawa211910.83
Magnús M. Halldórsson32436241.34
Atsuhiro Takasu441484.73
Keisuke Tanaka527819.04