CPM 1994: Combinatorial Pattern Matching pp 75-86

# Alignment of trees — An alternative to tree edit

• Tao Jiang
• Lusheng Wang
• Kaizhong Zhang
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 807)

## Abstract

In this paper, we propose the alignment of trees as a measure of the similarity between two labeled trees. Both ordered and unordered trees are considered. An algorithm is designed for ordered trees. The time complexity of this algorithm is OT1¦· s¦T2· (deg(T1) + deg(T2))2), where ¦Ti¦ is the number of nodes in T i and deg(T i ) is the degree of T i , i=1,2. The algorithm is faster than the best known algorithm for tree edit when deg(T1) and deg(T2) are smaller than the depths of T1 and T2. For unordered trees, we show that the alignment problem can be solved in polynomial time if the trees have a bounded degree and becomes NP-hard if one of the trees is allowed to have an arbitrary degree. In contrast, the edit problem for unordered trees is NP-hard even if both trees have a bounded degree [17]. Finally, multiple alignment of trees is discussed.

## Keywords

Lower Segment Optimal Alignment Edit Operation Label Tree Arbitrary Degree
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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## Authors and Affiliations

• Tao Jiang
• 1
• Lusheng Wang
• 2
• Kaizhong Zhang
• 3
1. 1.Department of Computer ScienceMcMaster UniversityHamiltonCanada
2. 2.Department of Electrical and Computer EngineeringMcMaster UniversityHamiltonCanada
3. 3.Department of Computer ScienceUniversity of Western OntarioLondonCanada