On the editing distance between unordered labeled trees
Information Processing Letters
Network flows: theory, algorithms, and applications
Network flows: theory, algorithms, and applications
Some MAX SNP-hard results concerning unordered labeled trees
Information Processing Letters
Alignment of trees: an alternative to tree edit
Theoretical Computer Science
Ordered and Unordered Tree Inclusion
SIAM Journal on Computing
The hardness of approximation: gap location
Computational Complexity
The Tree-to-Tree Correction Problem
Journal of the ACM (JACM)
On the approximation of largest common subtrees and largest common point sets
Theoretical Computer Science
Approximation and Special Cases of Common Subtrees and Editing Distance
ISAAC '96 Proceedings of the 7th International Symposium on Algorithms and Computation
A survey on tree edit distance and related problems
Theoretical Computer Science
SIAM Journal on Computing
System for the analysis and visualization of large 3D anatomical trees
Computers in Biology and Medicine
Improved approximation of the largest common subtree of two unordered trees of bounded height
Information Processing Letters
Algorithms in Bioinformatics: A Practical Introduction
Algorithms in Bioinformatics: A Practical Introduction
Constant Factor Approximation of Edit Distance of Bounded Height Unordered Trees
SPIRE '09 Proceedings of the 16th International Symposium on String Processing and Information Retrieval
An optimal decomposition algorithm for tree edit distance
ACM Transactions on Algorithms (TALG)
Exact algorithms for computing the tree edit distance between unordered trees
Theoretical Computer Science
Improved MAX SNP-hard results for finding an edit distance between unordered trees
CPM'11 Proceedings of the 22nd annual conference on Combinatorial pattern matching
On tree-constrained matchings and generalizations
ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
Efficient exponential time algorithms for edit distance between unordered trees
CPM'12 Proceedings of the 23rd Annual conference on Combinatorial Pattern Matching
Neighborhood-Preserving mapping between trees
WADS'13 Proceedings of the 13th international conference on Algorithms and Data Structures
On the complexity of finding a largest common subtree of bounded degree
FCT'13 Proceedings of the 19th international conference on Fundamentals of Computation Theory
Efficient exponential-time algorithms for edit distance between unordered trees
Journal of Discrete Algorithms
Hi-index | 5.23 |
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.