This is the nineteenth edition of a (usually) quarterly column that covers new developments in the theory of NP-completeness. 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 NP-Completeness,’ ’ 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, cross-references will be given to that book and the list of problems (NP-complete and harder) presented there. Readers who have results they would like mentioned (NP-hardness, PSPACE-hardness, polynomial-time-solvability, etc.) or open problems they would like publicized, should

We have been developing a theory for the generic representation of 2-D 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...

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Computing the least common subsumer (lcs) is an inference task that can be used to support the "bottom-up " 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.

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 "table-of-contents" 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 non-trivial way and traditional data mining frameworks are inapplicable. We define this discovery problem and propose a solution. 1 Introduction 1.1 Motivation Many on-line 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 ...

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

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 D-equivalence, 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 D-equivalent 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 D-equivalent is coNP-hard.

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.

We consider the use of medial surfaces to represent symmetries of 3-D 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 3-D object model retrieval. Our formulation uses the geometric information

. We state precise definitions of the basic notions of Sowa's framework [Sowa 84] and provide related results. These results mainly concern the structure of the specialization relation, correspondence between graph operations and logical operations, and algorithmic complexity of the model handling. RESUME. Nous dfinissons prcisment les notions de base du modle des graphes conceptuels de Sowa [Sowa 84] et en tudions les proprits. Nos rsultats portent principalement sur la structure de la relation de spcialisation, la correspondance entre oprations de graphes et oprations logiques, et la complexit algorithmique de la mise en oeuvre du modle. KEY WORDS : Knowledge representation, conceptual graphs, Sowa's graphs, semantic networks, specialization / generalization, graphs, pattern matching, first order logic, algorithmic complexity. MOTS-CLES : reprsentation de connaissances, graphes conceptuels, graphes de Sowa, rseaux smantiques, spcialisation / gnralisation, graphes, appariement, log...