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30
Shock Graphs and Shape Matching
, 1998
"... We have been developing a theory for the generic representation of 2D shape, where structural descriptions are derived from the shocks (singularities) of a curve evolution process, acting on bounding contours. We now apply the theory to the problem of shape matching. The shocks are organized into a ..."
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Cited by 203 (32 self)
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We have been developing a theory for the generic representation of 2D shape, where structural descriptions are derived from the shocks (singularities) of a curve evolution process, acting on bounding contours. We now apply the theory to the problem of shape matching. The shocks are organized into a directed, acyclic shock graph, and complexity is managed by attending to the most significant (central) shape components first. The space of all such graphs is highly structured and can be characterized by the rules of a shock graph grammar. The grammar permits a reduction of a shock graph to a unique rooted shock tree. We introduce a novel tree matching algorithm which finds the best set of corresponding nodes between two shock trees in polynomial time. Using a diverse database of shapes, we demonstrate our system's performance under articulation, occlusion, and changes in viewpoint. Keywords: shape representation; shape matching; shock graph; shock graph grammar; subgraph isomorphism. 1 I...
The NPcompleteness column: an ongoing guide
 Journal of Algorithms
, 1985
"... This is the nineteenth edition of a (usually) quarterly column that covers new developments in the theory of NPcompleteness. The presentation is modeled on that used by M. R. Garey and myself in our book ‘‘Computers and Intractability: A Guide to the Theory of NPCompleteness,’ ’ W. H. Freeman & Co ..."
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Cited by 188 (0 self)
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This is the nineteenth edition of a (usually) quarterly column that covers new developments in the theory of NPcompleteness. The presentation is modeled on that used by M. R. Garey and myself in our book ‘‘Computers and Intractability: A Guide to the Theory of NPCompleteness,’ ’ W. H. Freeman & Co., New York, 1979 (hereinafter referred to as ‘‘[G&J]’’; previous columns will be referred to by their dates). A background equivalent to that provided by [G&J] is assumed, and, when appropriate, crossreferences will be given to that book and the list of problems (NPcomplete and harder) presented there. Readers who have results they would like mentioned (NPhardness, PSPACEhardness, polynomialtimesolvability, etc.) or open problems they would like publicized, should
Matching Hierarchical Structures Using Association Graphs
 IEEE Transactions on Pattern Analysis and Machine Intelligence
, 1998
"... this article, please send email to: tpami@computer.org, and reference IEEECS Log Number 108453 ..."
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Cited by 166 (26 self)
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this article, please send email to: tpami@computer.org, and reference IEEECS Log Number 108453
Computing Least Common Subsumers in Description Logics with Existential Restrictions
, 1999
"... Computing the least common subsumer (lcs) is an inference task that can be used to support the "bottomup " construction of knowledge bases for KR systems based on description logics. Previous work on how to compute the lcs has concentrated on description logics that allow for universal va ..."
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Cited by 89 (24 self)
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Computing the least common subsumer (lcs) is an inference task that can be used to support the "bottomup " construction of knowledge bases for KR systems based on description logics. Previous work on how to compute the lcs has concentrated on description logics that allow for universal value restrictions, but not for existential restrictions. The main new contribution of this paper is the treatment of description logics with existential restrictions. Our approach for computing the lcs is based on an appropriate representation of concept descriptions by certain trees, and a characterization of subsumption by homomorphisms between these trees. The lcs operation then corresponds to the product operation on trees.
Discovering Structural Association of Semistructured Data
, 1999
"... Many semistructured objects are similarly, though not identically, structured. We study the problem of discovering "typical" substructures of a collection of semistructured objects. The discovered structures can serve the following purposes: (a) the "tableofcontents" for gaining general informa ..."
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Cited by 60 (1 self)
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Many semistructured objects are similarly, though not identically, structured. We study the problem of discovering "typical" substructures of a collection of semistructured objects. The discovered structures can serve the following purposes: (a) the "tableofcontents" for gaining general information of a source, (b) a road map for browsing and querying information sources, (c) a basis for clustering documents, (d) partial schemas for providing standard database access methods, (e) user/customer's interests and browsing patterns. The discovery task is impacted by structural features of semistructured data in a nontrivial way and traditional data mining frameworks are inapplicable. We define this discovery problem and propose a solution. 1 Introduction 1.1 Motivation Many online documents, such as HTML, Latex, BibTex, SGML files and those found in digital libraries, are semistructured. Semistructured data arises when the source does not impose a rigid structure (such as the ...
Efficient discovery of frequent unordered trees
 In First International Workshop on Mining Graphs, Trees and Sequences
, 2003
"... Abstract. Recently, an algorithm called Freqt was introduced which enumerates all frequent induced subtrees in an ordered data tree. We propose a new algorithm for mining unordered frequent induced subtrees. We show that the complexity of enumerating unordered trees is not higher than the complexity ..."
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Cited by 41 (3 self)
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Abstract. Recently, an algorithm called Freqt was introduced which enumerates all frequent induced subtrees in an ordered data tree. We propose a new algorithm for mining unordered frequent induced subtrees. We show that the complexity of enumerating unordered trees is not higher than the complexity of enumerating ordered trees; a strategy for determining the frequency of unordered trees is introduced. 1
Minimising Simple XPath Expressions
 In WebDB
, 2001
"... We consider a subset of XPath expressions, called simple XPath expressions, which correspond to a class of conjunctive queries. We show that, in the absence of a DTD, each simple XPath expression has a unique minimal equivalent expression which can be found in polynomial time. We then consider Dequ ..."
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Cited by 39 (6 self)
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We consider a subset of XPath expressions, called simple XPath expressions, which correspond to a class of conjunctive queries. We show that, in the absence of a DTD, each simple XPath expression has a unique minimal equivalent expression which can be found in polynomial time. We then consider Dequivalence, the equivalence of expressions with respect to the set of documents valid for a given DTD D. We show that a simple XPath expression P does not necessarily have a unique minimal Dequivalent expression. However, if P is reduced (there are no wildcards in it), then there is a unique minimal equivalent expression, but we show that deciding whether two reduced expressions are Dequivalent is coNPhard.
Retrieving articulated 3D models using medial surfaces
, 2008
"... We consider the use of medial surfaces to represent symmetries of 3D objects. This allows for a qualitative abstraction based on a directed acyclic graph of components and also a degree of invariance to a variety of transformations including the articulation of parts. We demonstrate the use of this ..."
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Cited by 37 (2 self)
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We consider the use of medial surfaces to represent symmetries of 3D objects. This allows for a qualitative abstraction based on a directed acyclic graph of components and also a degree of invariance to a variety of transformations including the articulation of parts. We demonstrate the use of this representation for 3D object model retrieval. Our formulation uses the geometric information
Frequent Subtree Mining  An Overview
, 2005
"... Mining frequent subtrees from databases of labeled trees is a new research field that has many practical applications in areas such as computer networks, Web mining, bioinformatics, XML document mining, etc. These applications share a requirement for the more expressive power of labeled trees to ..."
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Cited by 34 (3 self)
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Mining frequent subtrees from databases of labeled trees is a new research field that has many practical applications in areas such as computer networks, Web mining, bioinformatics, XML document mining, etc. These applications share a requirement for the more expressive power of labeled trees to capture the complex relations among data entities. Although frequent subtree mining is a more difficult task than frequent itemset mining, most existing frequent subtree mining algorithms borrow techniques from the relatively mature association rule mining area. This paper provides an overview of a broad range of tree mining algorithms. We focus on the common theoretical foundations of the current frequent subtree mining algorithms and their relationship with their counterparts in frequent itemset mining. When comparing the algorithms, we categorize them according to their problem definitions and the techniques employed for solving various subtasks of the subtree mining problem. In addition, we also present a thorough performance study for a representative family of algorithms.
Finding Largest Subtrees and Smallest Supertrees
 Algorithmica
, 1998
"... As trees are used in a wide variety of application areas, the comparison of trees arises in many guises. Here we consider two generalizations of classical tree pattern matching, which consists of determining if one tree is isomorphic to a subgraph of another. For the embedding problems of subgraph i ..."
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Cited by 21 (1 self)
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As trees are used in a wide variety of application areas, the comparison of trees arises in many guises. Here we consider two generalizations of classical tree pattern matching, which consists of determining if one tree is isomorphic to a subgraph of another. For the embedding problems of subgraph isomorphism and topological embedding, we present algorithms for determining the largest tree embeddable in two trees T and T 0 (or a largest subtree) and for constructing the smallest tree in which each of T and T 0 can be embedded (or a smallest supertree). Both subtrees and supertrees can be used in a variety of different applications. For example, when each of the two trees contains partial information about a data set, such as the evolution of a set of species, the subtree or supertree corresponds to a structuring of the data in a manner consistent with both original trees. The size of a subtree or supertree of two trees can also be used to measure the similarity between two arrangem...