K. Zhang, D. Shasha, and J. T. L. Wang. Approximate tree matching in the presence of variable length don't cares. J. Algorithms, 16(1):33--66, 1994.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....) #(P, cut(T , C) Where both P and T are trees. Intuitively, this is the distance between the pattern tree and the cut data tree, where the cut yields the smallest possible distance. The more general concept which has many applications in querying the SGML documents is introduced in [20]. Suppose some of nodes have one of the two labels: and #. A node with label in the pattern tree can substitute part of a path from the root to a leaf of the data tree. A node with # in the pattern tree can substitute part of such path and all the subtrees emanating from the nodes of ....

....we get another tree P in T, however still P is di#erent from T . The approximate matching between P and T w.r.t. s, is defined as tree vldc(P, T , s) tree cut(P , T ) Then, tree vldc(P, T ) min s#S tree vldc(P, T , s) Where S is the set of all possible substitutions. In [20] again by deriving the similar formulae to lemmas 1 3, the author could design a dynamic algorithm. Also, in this paper, you can find other generalization of this problem. 6 Generalization In this section, we discuss comparing of other structures than ordered labeled tree introduced in ....

K. Zhang, D. Shasha, J. T. Wang, "Approximate tree matching in the presence of variable length don't cares", Journal of algorithms 16, 1994, 33-66.

....between two trees. The rightmost diagram includes a sequence of edit operations not constituting a mapping. 3 The Zhang and Shasha s Algorithm We have based our work in the Zhang and Shasha s tree pattern matching algorithm, introduced in [8] and extended with advanced matching features in [9]. A major characteristic of this algorithm is its bottom up oriented approach. Given the l keyroots(T ) the set of all nodes in T which have a left sibling plus the root, 3 a b c d e f g a b c d e g f a b c d e f g a b c d e g f Fig. 1. An example on mappings j i h c g b f e T[1. 8] d h i j ....

Zhang, K. and Shasha, D. and Wang, J.T.L. Approximate Tree Matching in the Presence of Variable Length Don't Cares. Journal of Algorithms, pages 33-66, vol 16 (1), 1994

....to share common parts. Although in the case of the query, language ambiguity could probably be eliminated, queries could vary widely from indexes or some structural details are unknown, and an approximate matching strategy in the presence of variable length don t cares (vldc) becomes necessary [10]. Previous works do not provide a mechanism to fully exploit structural sharing in vldc matching. Our aim is to cover the lack of proposals in this domain. 2 The editing distance Given P , a pattern tree, and D, a data tree, we de ne an edit operation as a pair a b; a 2 labels(P ) f g; b 2 ....

....4 2 5 6 7 j d h i c g T[1. 8] e f d h i j T[1. 4] Fig. 1. The forest distance using an inverse postorder numbering In dealing with approximate vldc pattern matching, some structural details can be omitted in the target tree and di erent strategies are then applicable. Following Zhang et al. in [10] we introduce two di erent de nitions to vldc matching: The vldc substitutes for part of a path from the root to a leaf of the data tree. We represent such a substitution, shown in Fig. 2, by a vertical bar j , and call it a path vldc. The vldc matches part of such a path and all the ....

[Article contains additional citation context not shown here]

Zhang, K. and Shasha, D. and Wang, J.T.L. Approximate Tree Matching in the Presence of Variable Length Don't Cares. Journal of Algorithms, pages 33-66, vol 16 (1), 1994

....5 6 7 j d h i c g T[1. 8] e f d h i j T[1. 4] Figure 1: The forest distance using an inverse postorder numbering In dealing with approximate vldc pattern matching, some structural details can be omitted in the target tree and different strategies are then applicable. Following Zhang et al. in [7] we introduce two different definitions to vldc matching: ffl The vldc substitutes for part of a path from the root to a leaf of the data tree. We represent such a substitution, shown in Fig. 2, by a vertical bar j , and call it a path vldc. ffl The vldc matches part of such a path and all the ....

.... c d e f g a b c d e g f a b d g a b c d e g f a b c d e g a b c d e g f a b d g a b c d e g f Mapping without VLDC Mapping with a Path VLDC Mapping with an Umbrella VLDC Correct Incorrect Figure 2: An example on mappings 4 Approximate vldc tree matching The major question of Zhang et al. in [7], is the tree distance algorithm itself. However, parsing and tree to tree correction are topologically related and, to get the best performance, it is necessary to understand the mechanisms that cause the phenomenon of tree duplication. A major factor to take into account is the syntactic ....

[Article contains additional citation context not shown here]

K. Zhang, D. Shasha, and J. T. L. Wang. Approximate tree matching in the presence of variable length don't cares. Journal of Algorithms, 16(1):33--66, Jan. 1994.

.... and ordered region inclusion are solvable in time O(mn) 2 Tree inclusion problems can be considered to be special cases of the editing distance problem for trees [Tai79, ZS89] Ordered tree inclusion problems can be described and solved in the framework of Zhang, Shasha, Wang, and Jeong [ZSW91, WJZS91] They allow patterns to contain variable length don t care symbols (VLDCs) A path VLDC is a pseudo node in the pattern that matches at an arbitrary path in the target. The algorithms of [ZSW91, WJZS91] allow tree matching with cut: the instances of the pattern are the subtrees of the ....

....problems can be described and solved in the framework of Zhang, Shasha, Wang, and Jeong [ZSW91, WJZS91] They allow patterns to contain variable length don t care symbols (VLDCs) A path VLDC is a pseudo node in the pattern that matches at an arbitrary path in the target. The algorithms of [ZSW91, WJZS91] allow tree matching with cut: the instances of the pattern are the subtrees of the target that are identical with the pattern after deleting the nodes matched with the VLDCs and possibly cutting at some nodes. Therefore, the ordered tree inclusion problem can be presented as a matching ....

[Article contains additional citation context not shown here]

K. Zhang, D. Shasha, and J. T.-L. Wang. Approximate tree matching in the presence of variable length don't cares. Submitted for publication, July 1991.

....for zero or more letters in S at zero cost. The dissimilarity measure used in comparing two sequences is the edit distance, i.e. the minimum weighted number of insertions, deletions and substitutions used to transform one sequence to the other after an optimal substitution for the VLDCs [86, 95]. The edit distance is a useful measure of evolutionary distance [11, 84] For the purpose of this work, we assume that all the edit operations have unit cost, though the techniques we propose do not depend on that cost assumption or essentially on the edit distance metric. Example 2.1 (Matching ....

....better than the best classifier available today and provide complementary information to them, thus indicating the potential of the proposed methods. 10.2 Future Works The work described here is part of a project for pattern matching and discovery in scientific, program and document databases [73, 74, 89, 90, 91, 95]. Our future works will focus on: ffl Application of our pattern discovery techniques to trees and graphs and using the discovered patterns to do classification of RNA secondary structures (represented as trees) 15, 49, 53, 55] ffl Development of the discovering algorithms for high dimensional ....

K. Zhang, D. Shasha, and J. T. L. Wang, "Approximate tree matching in the presence of variable length don't cares," Journal of Algorithms, vol. 16, no. 1, pp. 33--66, January 1994.

....of temperature data. The bulk types sequence, tree, and multidimensional array all fall beyond the power of relational and most current object oriented query languages, and severely stress the query facilities of object oriented database systems. As yet, only a small amount of work has been done [18, 47, 57, 61, 62] to extend the power of query languages to include these and other bulk types. It is important to have a single query capability that can be used to access all the information of interest. Object oriented database systems are based on flexible, extensible type systems and thus provide a good basis ....

Kaizhong Zhang, Dennis Shasha, and Jason T. L. Wang. Approximate Tree Matching in the Presence of Variable Length Don't Cares. Journal of Algorithms, 15, 1993.

.... don t cares was studied by Fisher and Paterson [4] A lot of studies have been done for approximate string matching [5] Myers and Miller studied approximate string matching of regular expressions [7] and Zhang, Shasha and Wang studied approximate tree matching with variable length don t cares [8]. Although these two studies are close to our problem, the ranges of lengths of don t cares can not be specified. Exact string matching with variable length don t cares was studied by Manber and Baeza Yates [6] In their work, the range can be specified, but approximate matching was not ....

K. Zhang, D. Shasha, and J. Wang, "Approximate tree matching in the presence of variable length don't cares," Journal of Algorithms, vol.16, pp.33--66, 1994.

....document. For example, the template tree in Figure 3 does not match the memorandum HDT in Figure 2 exactly. This paper presents an approximate tree matching approach by tree transformation. Tree Transformation Operations In the proposed approach, three transformation operations: insert, delete (Zhang, Shasha, Wang 1994), and copy are defined. The first operation is used to transform HDTs, while the other two are for template trees. Given a tree H = hN; Child i. Let n be an internal node n 2 N with Child(n) c 1 ; c 2 ; c k . The result of Insert(c i ; c j ) creates a new node c 0 such that (where 1 ....

....3, the copy operation is applied at steps 1. b) and 2. b) Theorem 1 The proposed tree matching is both sound and complete. That is, it is guaranteed to find a match if one exists, and the match it does find satisfies Definition 6. The proofs are based on the proofs for the algorithm in (Zhang, Shasha, Wang 1994). On the other hand, the algorithm is not guaranteed to find the optimal match. In this approach, a match is considered to be the best if the copy operation is applied to T as many times as possible. Algorithm 2 Deciding if two lists of nodes can match. GroupMatch (list of template nodes T = t ....

Zhang, K.; Shasha, D.; and Wang, J. 1994. Approximate tree matching in the presence of variable length don't cares. Journal of Algorithms 16:33--66.

....1995 To appear in Proc. 11th Intl. Conf. on Data Engg. 1995 timization techniques, free composability with other algebra operators, and extensibility. We do not assume any particular user level language, but we note that our extensions to AQUA can model the user level language described in [35,36]. The AQUA list and tree algebras have a small number of primitive operators which can be used to build other useful operators. Query operations frequently filter out some elements of a collection type. In an ordered structure, we want to ensure that such filtering preserves the order of the ....

....These papers, however, do not address the issue of more general trees. An algebra for queries on sequences is presented in [27] but this algebra does not address patternmatching (its predicates are applied to one node at a time) All of the operators result in a single sequence. Recent work [35,36] on approximate tree matching discusses tree algebras targeted towards problems in vision and molecular biology. These papers propose various distance metrics for trees. These metrics are useful in answering queries such as give me all the subtrees of T which almost satisfy pattern P . Such ....

K. Zhang, D. Shasha, and J. T. L. Wang, "Approximate Tree Matching in the Presence of Variable Length Don't Cares,"

....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 T-L. Wang. Approximate tree matching in the presence of variable length don't cares. Journal of Algorithms, (to appear).

....in the HDT. A variable type node may match node in the original HDT or a newly inserted node. The HDT subtree rooted at the node that matches a variable type node represents the information captured. 5.4. 4 Tree Matching Algorithm The matching algorithm is based on the idea of breadth first search [23]. Both the Template Tree and HDT are traversed in a breadth first fashion concurrently while looking for a match. Deciding which HDT node(s) can match an exact type template node or a compound type node is quite straightforward. However, there could be multiple ways to match a variable type node ....

K. Zhang, D. Shasha, and Wang J. T. L. Approximate tree matching in the presence of variable length don't cares. Journal of Algorithms, 16(1):33--66, 1994.

No context found.

Zhang K., Shasha D. and Wang, J., Approximate Tree Matching in the Presence of Variable Length don't Cares. Journal of Algorithms, 16(1):33-66, January 1994.

No context found.

K. Zhang, D. Shasha, and J. T. L. Wang. Approximate tree matching in the presence of variable length don't cares. Journal of Algorithms, 16(1):33-66, 1994. 9

....e Trees: Paths: Q Figure 1: Example trees. In practice, it s likely that some portion of a query tree is unknown, uninteresting or unimportant. That portion is often represented by a don t care symbol. In general, there are two types of don t care symbols: variable length don t cares (VLDCs) [22, 26] and xed length don t cares (FLDCs) In string matching, a VLDC, denoted , in the query string may substitute for zero or more characters in a data string. For example, if com er is the query string, then the would substitute for the substring put when matching with the data string ....

K. Zhang, D. Shasha, and J. T. L. Wang. Approximate tree matching in the presence of variable length don't cares. Journal of Algorithms, 16(1):33-66, 1994.

....Now consider the query supported by the select operator in AQUA [86] Find all nodes (persons) who are ancestors of Alex and also descendants of Mary. This query could be expressed by a tree pattern, as shown in Figure 2(b) The node in the tree pattern is a variable length don t care (VLDC) [93, 106], which would be instantiated into (matched with) a path of nodes of a data tree at no cost. In our example, the nodes in the family tree matched by the VLDC (here, Bill and Adam) would be returned as answers to the query. The preceding queries share some characteristics. Mary John Mary ....

K. Zhang, D. Shasha, and J. T. L. Wang. Approximate tree matching in the presence of variable length don't cares. Journal of Algorithms, 16(1):33-66, 1994.

.... nodes) We believe the presented techniques can also contribute to comparison and search of 2 D and 3 D (macro)molecules in protein and DNA structures [14] Comparison to Past Research This paper generalizes the work on the edit distance between strings [6, 11, 13, 16, 20, 21, 25] and trees [19, 28, 29]. Various kinds of constrained and generalized edit distance on strings and trees have been developed [1, 9, 10, 17, 27] Our degree 2 distance, when applied to unordered trees, is a restricted form of the constrained distance previously reported in [27] When applied to ordered trees, the ....

K. Zhang, D. Shasha, and J. T. L. Wang. Approximate tree matching in the presence of variable length don't cares. Journal of Algorithms, 16(1):33--66, Jan. 1994. 11

....of VLDC s in strings, and formulated the problems of approximate tree matching with the VLDC s. We then introduced a new suffix forest distance measure for solving the problems. Our algorithms differ in the particular semantics they give to the VLDC s, but share the same time complexity. In [26,27], we presented a parallel version of the algorithms. In our toolkit [23,24] we have found that these algorithms work very well in practice too. In fact, the toolkit also generates a best mapping having the distance between the pattern and the data trees, still preserving the time complexity. 8 ....

K. Zhang, D. Shasha, and J. T. L. Wang. Approximate tree matching in the presence of variable length don't cares. Technical Report TR-328, Department of Computer Science, The University of Western Ontario, 1992.

....candidate motifs. Then we calculated the occurrence number 2 of each candidate motif M by adding variable length don t cares (VLDCs) to M as the new root and leaves to form a VLDC pattern V and then comparing V with each tree T in the file using the pattern matching technique developed in [26]. A VLDC (conventionally denoted by ) can be matched, at no cost, with a path or portion of a path in T . The technique calculates the minimum distance between V and T after implicitly computing an optimal substitution for the VLDCs in V , allowing zero or more cuttings at nodes from T (see ....

K. Zhang, D. Shasha, and J. T. L. Wang. Approximate tree matching in the presence of variable length don't cares. Journal of Algorithms, 16(1):33--66, Jan. 1994.

....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. It is open whether the time ....

Zhang, K., D. Shasha, and J.T.L. Wang [1994]. "Approximate tree matching in the presence of variable length don't cares", J. of Algorithms, 16, pp.33-66.

No context found.

K. Zhang, D. Shasha, and J. T. L. Wang. Approximate tree matching in the presence of variable length don't cares. J. Algorithms, 16(1):33--66, 1994.

No context found.

K. Zhang, D. Shasha, and J.T.L. Wang. Approximate tree matching in the presence of variable length don't cares. Journal of Algorithms, 16(1):33-66, January 1994.

No context found.

Kaizhong Zhang, Dennis Shasha, and Jason T. L. Wang. Approximate tree matching in the presence of variable length don't cares. Journal of Algorithms, 16(1):33--66, 1994.

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC