K. Zhang, R. Statman and D. Shasha, "On the editing distance between unordered labeled trees" Information Processing Letters, 42 (1992), p. 133-139. 7  Home/Search   Document Not in Database   Summary   Related Articles   Check

....is a classical example of a problem with vast computational complexity interestingly, it has still not been proven to be NP complete [4] As trees are only a subclass of graphs, one might think that tree matching would be much easier than general graph matching. However, it has been shown [11] that calculating difference of two unordered attribute trees (which implicitly requires an optimal match) is an NP complete problem. Alternatively, one may use syntactic methods in classifying graphs [1] In this study, we assume that the size is an essential property of a tree, and expect the ....

K. Zhang, R. Statman, and D. Shasha. On the editing distance between unordered labeled trees. Information Processing Letters, 42(3):133--139, 1992.

....structure is so appropriate for the case that the order of children is not important in the hierarchial structure, e.g. in documents that each node is an item and has only unordered sub items. The edit distance for these graphs is defined similarly to our definition for ordered labeled trees. In [21] has been shown that computing the edit distance for unordered labeled trees in NP complete, but still we would like to find the distances that can be e#ciently computed. 16] considers a constrained edit distance metric between unordered labeled trees. The constraint is a natural one, namely, ....

....of labeled trees without ordering which is a special case of AOLT, is NP complete. However, ALOT structures are often used in modeling of SGML documents in which some of the vertices have ordering, and some doesn t have. Constrained edit distance was restriction that enabled the authors in [21] to solve this problem. Another restriction which seems logical is that the maximum degree in SGML documents are not so large (in must of the case we can assume that it is less than 7) It seems that if we consider the case in which degree of each vertex is at most a constant C, then we would be ....

K. Zhang, R. Statman, D. Shasha, "On the editing distance between unordered labeled trees", Information Processing letters 42, 1992, 133-139.

....is more important. Thus, X Diff is designed to handle unordered tree representations of XML documents. This is the major difference between our work and earlier efforts in this area [4, 5] High Performance. Change detection on unordered trees is substantially harder than that on ordered trees; [21] has shown it to be NP Complete in general case. By exploiting certain features of XML documents, our algorithm achieves polynomial time in complexity. The remainder of the paper is organized as follows. Related work is contained in Section 2. In Section 3, we formulate the problem and give an ....

....the two trees, its use conflicts with the cost model employed by Zhang and Shasha s algorithm. Thus, XMLTreeDiff may not generate an optimal result. Both [4] and [5] focus on change detection for ordered trees. On the other hand, there are very few algorithms capable of handling unordered trees. [21] proved that general unordered tree to tree correction problem is NP complete. Zhang proposed a polynomial time algorithm based on a restriction that matching is only performed between nodes at the same level [22] As mentioned in the previous section, XML documents have more features than general ....

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K. Zhang, R. Statman, D. Shasha, "On the Editing Distance between Unordered Labeled Trees", Information Processing Letters, 42: 133-139, 1992.

....represents the immediate enclosure relation between the two edges (see fig. 1) a b c d d = parent(a) Figure 1: Secondary structure of an RNA sequence Consequently, much of the work on comparing the secondary structures of two RNA strings have been modeled as problems of comparing two trees [7, 22, 25, 26]. In this paper, we study several problems in computing the similarity between two RNA strings that take into consideration both the primary sequence and secondary base pairing information provided with the strings. We also investigate the problem of inferring the secondary structure of an RNA ....

....our formulation of the prediction problem appears increasingly relevant. Related work Comparison methods. First we review work on comparison methods developed to estimate distances between RNA secondary structures. Since secondary structures can be represented as trees, there are several papers [7, 22, 25, 26] addressing comparisons of trees. Tree edits are discussed and efficient algorithms are derived in [22, 25, 26] while a new notion of tree alignment is proposed and algorithms developed in [7] Even though these comparison methods compute distances only between secondary structures, the worst case ....

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K. Zhang, R. Statman, and D. Shasha, "On the editing distance between unordered labeled trees," Inform. Proc. Lett. 42, 133-139 (1992).

....string matching to trees; these problems involve nding a modi ed version of a pattern tree in a text tree. For some applications, comparison of unordered trees would make more sense. 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. One might consider generalizing from edit distance between ordered trees to edit distance between planar graphs. However, the problem of nding a Hamiltonian path in a planar graph can be ....

K. Zhang, R. Statman and D. Shasha, \On the editing distance between unordered labeled trees," Information Processing Letters 42 (1992), pp. 133-139

....of comparing unrooted trees, i.e when there is no natural root in the trees. The time complexity of Klein s algorithm for the unrooted version is also O(n 3 log n) One can also consider the comparison of unordered trees; however, the edit distance between such trees is NP hard to compute [12]. Also, in view of the interpretation of ordered trees as embedded in the plane, one might consider the comparison of planar graphs; again, the edit distance problem is NP hard for such graphs [5] Variations on edit distance have also been considered, e.g. minimizing average cost per operation ....

K. Zhang, R. Statman and D. Shasha, \On the editing distance between unordered labeled trees," Information Processing Letters 42 (1992), pp. 133-139

....two strings ( 8] 9] 16] to labeled trees. The trees under consideration in the tree editing problem are ordered, i.e. the left to right order of the children of a node is significant. Without this assumption, i.e. if considering unordered trees, the tree editing problem becomes NP complete [19]. The edit operations available in the tree editing problem are changing, deleting and inserting a node. To these operations costs are assigned that depend on the labels of the This work was supported by the DFG under grant Bl 320 2 1 nodes involved. The problem is to find a sequence of ....

K. Zhang, R. Statman and D. Shasha, On the editing distance between unordered labeled trees, IPL 42 (1992), pp. 133 - 139.

....depending on how the temporary arrays are implemented, in O(nm) An example which illustrates this algorithm and compares it to our solution is given below. This work has been extended by the inclusion of more general pattern matching, and the development of programs that implement the algorithms [13, 14, 15, 16, 17, 18]. Notational conventions are: T i in this algorithm only: the ith node of T , labelled in post order l(i) the leftmost leaf descendant of the subtree rooted at i K(T ) the keyroots of tree T , K(T ) fk ....

D. Shasha, K. Zhang, and R. Statman. On the editing distance between unordered labeled trees. Information Processing Letters, 42:133--139, 1992.

....integer DIFF , a query tree Q and a database D of trees, the ANN problem is to nd all the data trees D in D where D approximately contains Q within distance DIFF . That is, D contains a substructure D and the distance from Q to D is at most DIFF . We proved that this problem was NP complete [27] for edit distance. So we adopt a di erent method. We measure the distance from Q to D by the total number of root to leaf paths in Q that do not appear in D ; the nodes in D that do not appear in Q can be freely removed. To our knowledge, no previous work has addressed the ANN problem ....

K. Zhang, R. Statman, and D. Shasha. On the editing distance between unordered labeled trees. Information Processing Letters, 42:133-139, 1992. 19

....can be expressed by a containment mapping. That is, one asks whether the query tree appears, or approximately appears, in a data tree. Here, the approximation is measured by the number of paths in the query tree that do not appear in the data tree [84] or by some other distance functions [22, 23, 24, 85, 96, 104, 107]. The query tree may contain don t cares or wildcards [72] There are xed length don t cares (FLDCs) that may match a single node and variable length don t cares (VLDCs) 84] We shall refer to this class of queries as approximate containment (AC) queries. In general, a query ....

K. Zhang, R. Statman, and D. Shasha. On the editing distance between unordered labeled trees. Information Processing Letters, 42:133-139, 1992.

....attention recently in the literature. There are several ways to represent RNA structures and formulate corresponding similarity measures. One of them is to represent RNA secondary structures as (labeled or unlabeled) trees. There are several algorithms for computing the distance between two trees [19, 21, 24, 20, 25, 23, 22]. Another method for modeling RNA structures is using stochastic context free grammars (SCFGs) which is a generalization of hidden Markov models (HMMs) capturing well the common primary and secondary structures [16, 4] Notice that the above two methods do not treat basepairs as units of ....

K. Zhang, R. Statman, and D. Shasha. On the editing distance between unordered labeled trees. Information Processing Letters, 42:133-139, 1992. Edit Distance between RNA Structures 21

....Thus, the user can modify those routines without changing the rest of the system. The modular design also facilitates augmenting the system with additional functions. Work on ATBE is continuing. We have two main goals. 1. Our system, as well as our algorithms, deal with ordered, labeled trees. In [48], it was shown that the problem of finding the editing distance between unordered, labeled trees (i.e. trees in which the left toright order of each node s children is unimportant) is NP complete. We are investigating heuristics for comparing these trees, and plan to extend our system to handle ....

K. Zhang, R. Statman, and D. Shasha, "On the editing distance between unordered labeled trees," Information Processing Letters, in press.

....preserving mapping and gave an algorithm based on this kind mapping. Their algorithm is the same as Lu s algorithm. Yang [1991] gave an algorithm based on a mapping where two nodes in the mapping implies their parents are in the mapping. Edit distance between unordered tree was considered by Zhang, Statman and Shasha [1992]. Jiang, Wang and Zhang [1994] considered the tree alignment distance problem. Tree inclusion problem was introduced by Kilpelainen and Mannila. The algorithm for edit distance presented in this chapter is due to Zhang and Shasha. The alignment distance algorithm is due to Jiang, Wang and Zhang. ....

Zhang, K., R. Statman and D. Shasha [1992]. "On the editing distance between unordered labeled trees" Information Processing Letters 42, pp.133-139.

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K. Zhang, R. Statman and D. Shasha, "On the editing distance between unordered labeled trees" Information Processing Letters, 42 (1992), p. 133-139. 7

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Zhang, K., Statman, R., & Shasha, D. (1992). On the editing distance between unordered labeled trees. Information Processing Letters, 42(3), 133--139.

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Zhang, K., Statman, R., Shasha, D.: On the editing distance between unordered labeled trees. Inf. Process. Lett. 42 (1992) 133--139

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Kaizhong Zhang, Rick Statman, and Dennis Shasha. On the editing distance between unordered labeled trees. Inf. Process. Lett., 42(3):133--139, 1992.

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K. Zhang, R. Statman, and D. Shasha. On the editing distance between unordered labeled trees. Information Processing Letters, 42(3):133--139, 1992. 511

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Zhang, Z., Statman, R., and Shasha, D., On the editing distance between unordered labeled trees, Information Processing Letters, 42(3):133--139, 1992.

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ZHANG K., STATMAN R., SHASHA D., "On the editing distance between unordered labeled trees", Information Proceedings Letters 42, , 1992, p. 133-139.

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Zhang, K., Statman, R., Shasha, D.: On the editing distance between unordered labeled trees. Information Processing Letters 42 (1992) 133--139

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Kaizhong Zhang, Rick Statman, and Dennis Shasha. On the editing distance between unordered labeled trees. Information Processing Letters, 42:133--139, 1992.

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Kaizhong Zhang, Rick Statman, and Dennis Shasha. On the editing distance between unordered labeled trees. Technical Report 289, The University of Western Ontario, Departement of Computer Science, 1991.

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Zhang, K., Statman, R., Shasha, D.: On the editing distance between unordered labeled trees. Information Processing Letters 42 (1992) 133--139

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K. Zhang, R. Statman, and D. Shasha. On the editing distance between unordered labeled trees. Information Proceedings Letters 42, pages 133--139, 1992.

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