On the editing distance between unordered labeled trees

Zhang, Kaizhong; Statman, Richard; Shasha, Dennis

doi:10.1016/0020-0190(92)90136-j

Cited by 269 publications

(180 citation statements)

References 3 publications

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“…Unfortunately, computing edit-distance on unordered trees is NP-complete, as shown by Zhang, Statman, and Shasha [12]. Zhang has given an algorithm [9] for computing a kind of constrained edit-distance between unordered trees.…”

Section: Related Problems On Treesmentioning

confidence: 99%

Computing the Edit-Distance Between Unrooted Ordered Trees

Klein

1998

Algorithms — ESA’ 98

177

175

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Abstract. An ordered tree is a tree in which each node's incident edges are cyclically ordered; think of the tree as being embedded in the plane. Let A and B be two ordered trees. The edit distance between A and B is the minimum cost of a sequence of operations (contract an edge, uncontract an edge, modify the label of an edge) needed to transform A into B. We give an O(n 3 log n) algorithm to compute the edit distance between two ordered trees.

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Section: Related Problems On Treesmentioning

confidence: 99%

Computing the Edit-Distance Between Unrooted Ordered Trees

Klein

1998

Algorithms — ESA’ 98

177

175

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“…Tree edit distance, or TED [1,11,16,22], is defined as the minimal total sum of costs of edit operations needed in order to turn the first tree into the second. In its most general form, TED is formulated for combinatorial trees T = (V, E, r) endowed with edge (or vertex) labels given by a mapping x : E → L , where L is a space of labels.…”

Section: Related Workmentioning

confidence: 99%

“…This means that we need to be able to compare unordered trees. Tree edit distance for unordered trees is generally NP complete to compute [1,22]. However, the classical proof of NP completeness is made for a particular case of edit distance with integer edit costs for trees with discrete labels, and it does not obviously carry over to the class of geometric trees.…”

Section: Introductionmentioning

confidence: 99%

Complexity of Computing Distances between Geometric Trees

Feragen

2012

Lecture Notes in Computer Science

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Abstract. Geometric trees can be formalized as unordered combinatorial trees whose edges are endowed with geometric information. Examples are skeleta of shapes from images; anatomical tree-structures such as blood vessels; or phylogenetic trees. An inter-tree distance measure is a basic prerequisite for many pattern recognition and machine learning methods to work on anatomical, phylogenetic or skeletal trees. Standard distance measures between trees, such as tree edit distance, can be readily translated to the geometric tree setting. It is well-known that the tree edit distance for unordered trees is generally NP complete to compute. However, the classical proof of NP completeness depends on a particular case of edit distance with integer edit costs for trees with discrete labels, and does not obviously carry over to the class of geometric trees. The reason is that edge geometry is encoded in continuous scalar or vector attributes, allowing for continuous edit paths from one tree to another, rather than finite, discrete edit sequences with discrete costs for discrete label sets. In this paper, we explain why the proof does not carry over directly to the continuous setting, and why it does not work for the important class of trees with scalar-valued edge attributes, such as edge length. We prove the NP completeness of tree edit distance and another natural distance measure, QED, for geometric trees with vector valued edge attributes.

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“…Here, an explanation component can help the user to adapt weights for the distance measure in order to reflect the individual notion of similarity. Zhang, Statman and Shasha, however, showed that computing the edit distance between unordered labeled trees is NP-complete [13]. Obviously, such a complex similarity measure is unsuitable for large databases.…”

Section: Definition 2 (Edit Distance)mentioning

confidence: 99%

“…Whereas the concept of feature vectors has proven to be very successful for unstructured content data, we particularly address the internal structure of similar objects. For this purpose we discuss several similarity measures for trees as proposed in the literature [1][2][3]. These measures are well suited for hierarchical objects and have been applied to web site analysis [4], structural similarity of XML documents [5], shape recognition [6] and chemical substructure search [4], for instance.…”

Section: Introductionmentioning

confidence: 99%

Efficient Similarity Search for Hierarchical Data in Large Databases

Kailing

Kriegel

Schönauer

et al. 2004

Lecture Notes in Computer Science

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Abstract. Structured and semi-structured object representations are getting more and more important for modern database applications. Examples for such data are hierarchical structures including chemical compounds, XML data or image data. As a key feature, database systems have to support the search for similar objects where it is important to take into account both the structure and the content features of the objects. A successful approach is to use the edit distance for tree structured data. As the computation of this measure is NP-complete, constrained edit distances have been successfully applied to trees. While yielding good results, they are still computationally complex and, therefore, of limited benefit for searching in large databases. In this paper, we propose a filter and refinement architecture to overcome this problem. We present a set of new filter methods for structural and for content-based information in tree-structured data as well as ways to flexibly combine different filter criteria. The efficiency of our methods, resulting from the good selectivity of the filters is demonstrated in extensive experiments with real-world applications.

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On the editing distance between unordered labeled trees

Cited by 269 publications

References 3 publications

Computing the Edit-Distance Between Unrooted Ordered Trees

Computing the Edit-Distance Between Unrooted Ordered Trees

Complexity of Computing Distances between Geometric Trees

Efficient Similarity Search for Hierarchical Data in Large Databases

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