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161
Learning Bayesian network structure from massive datasets: The “sparse candidate” algorithm
, 1999
"... Learning Bayesian networks is often cast as an optimization problem, where the computational task is to find a structure that maximizes a statistically motivated score. By and large, existing learning tools address this optimization problem using standard heuristic search techniques. Since the searc ..."
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Cited by 180 (9 self)
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Learning Bayesian networks is often cast as an optimization problem, where the computational task is to find a structure that maximizes a statistically motivated score. By and large, existing learning tools address this optimization problem using standard heuristic search techniques. Since the search space is extremely large, such search procedures can spend most of the time examining candidates that are extremely unreasonable. This problem becomes critical when we deal with data sets that are large either in the number of instances, or the number of attributes. In this paper, we introduce an algorithm that achieves faster learning by restricting the search space. This iterative algorithm restricts the parents of each variable to belong to a small subset of candidates. We then search for a network that satisfies these constraints. The learned network is then used for selecting better candidates for the next iteration. We evaluate this algorithm both on synthetic and reallife data. Our results show that it is significantly faster than alternative search procedures without loss of quality in the learned structures. 1
ConjunctiveQuery Containment and Constraint Satisfaction
 Journal of Computer and System Sciences
, 1998
"... Conjunctivequery containment is recognized as a fundamental problem in database query evaluation and optimization. At the same time, constraint satisfaction is recognized as a fundamental problem in artificial intelligence. What do conjunctivequery containment and constraint satisfaction have in c ..."
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Cited by 131 (13 self)
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Conjunctivequery containment is recognized as a fundamental problem in database query evaluation and optimization. At the same time, constraint satisfaction is recognized as a fundamental problem in artificial intelligence. What do conjunctivequery containment and constraint satisfaction have in common? Our main conceptual contribution in this paper is to point out that, despite their very different formulation, conjunctivequery containment and constraint satisfaction are essentially the same problem. The reason is that they can be recast as the following fundamental algebraic problem: given two finite relational structures A and B, is there a homomorphism h : A ! B? As formulated above, the homomorphism problem is uniform in the sense that both relational structures A and B are part of the input. By fixing the structure B, one obtains the following nonuniform problem: given a finite relational structure A, is there a homomorphism h : A ! B? In general, nonuniform tractability results do not uniformize. Thus, it is natural to ask: which tractable cases of nonuniform tractability results for constraint satisfaction and conjunctivequery containment do uniformize? Our main technical contribution in this paper is to show that several cases of tractable nonuniform constraint satisfaction problems do indeed uniformize. We exhibit three nonuniform tractability results that uniformize and, thus, give rise to polynomialtime solvable cases of constraint satisfaction and conjunctivequery containment.
HYPERTREE DECOMPOSITIONS AND TRACTABLE QUERIES
, 1998
"... Several important decision problems on conjunctive queries (CQs) are NPcomplete in general but become tractable, and actually highly parallelizable, if restricted to acyclic or nearly acyclic queries. Examples are the evaluation of Boolean CQs and query containment. These problems were shown tracta ..."
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Cited by 124 (30 self)
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Several important decision problems on conjunctive queries (CQs) are NPcomplete in general but become tractable, and actually highly parallelizable, if restricted to acyclic or nearly acyclic queries. Examples are the evaluation of Boolean CQs and query containment. These problems were shown tractable for conjunctive queries of bounded treewidth [7], and of bounded degree of cyclicity [18, 17]. The so far most general concept of nearly acyclic queries was the notion of queries of bounded querywidth introduced by Chekuri and Rajaraman [7]. While CQs of bounded query width are tractable, it remained unclear whether such queries are efficiently recognizable. Chekuri and Rajaraman [7] stated as an open problem whether for each constant k it can be determined in polynomial time if a query has query width ≤ k. We give a negative answer by proving this problem NPcomplete (specifically, for k = 4). In order to circumvent this difficulty, we introduce the new concept of hypertree decomposition of a query and the corresponding notion of hypertree width. We prove: (a) for each k, the class of queries with query width bounded by k is properly contained in the class of queries whose hypertree width is bounded by k; (b) unlike query width, constant hypertreewidth is efficiently recognizable; (c) Boolean queries of constant hypertree width can be efficiently evaluated.
Query Evaluation via TreeDecompositions
 JOURNAL OF THE ACM
, 2001
"... A number of efficient methods for evaluating firstorder and monadicsecond order queries on finite relational structures are based on treedecompositions of structures or queries. We systematically study these methods. In the first part of the paper we consider arbitrary formulas on treelike struc ..."
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Cited by 81 (15 self)
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A number of efficient methods for evaluating firstorder and monadicsecond order queries on finite relational structures are based on treedecompositions of structures or queries. We systematically study these methods. In the first part of the paper we consider arbitrary formulas on treelike structures. We generalize a theorem of Courcelle [8] by showing that on structures of bounded treewidth a monadic secondorder formula (with free first and secondorder variables) can be evaluated in time linear in the structure size plus the size of the output. In the second part we study treelike formulas on arbitrary structures. We generalize the notions of acyclicity and bounded treewidth from conjunctive queries to arbitrary firstorder formulas in a straightforward way and analyze the complexity of evaluating formulas of these fragments. Moreover, we show that the acyclic and bounded treewidth fragments have the same expressive power as the wellknown guarded fragment and the finitevariable fragments of firstorder logic, respectively.
Deciding FirstOrder Properties of Locally TreeDecomposable Graphs
 In Proc. 26th ICALP
, 1999
"... . We introduce the concept of a class of graphs being locally treedecomposable. There are numerous examples of locally treedecomposable classes, among them the class of planar graphs and all classes of bounded valence or of bounded treewidth. We show that for each locally treedecomposable cl ..."
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Cited by 75 (12 self)
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. We introduce the concept of a class of graphs being locally treedecomposable. There are numerous examples of locally treedecomposable classes, among them the class of planar graphs and all classes of bounded valence or of bounded treewidth. We show that for each locally treedecomposable class C of graphs and for each property ' of graphs that is denable in rstorder logic, there is a linear time algorithm deciding whether a given graph G 2 C has property '. 1 Introduction It is an important task in the theory of algorithms to nd feasible instances of otherwise intractable algorithmic problems. A notion that has turned out to be extremely useful in this context is that of treewidth of a graph. 3Colorability, Hamiltonicity, and many other NPcomplete properties of graphs can be decided in linear time when restricted to graphs whose treewidth is bounded by a xed constant (see [Bod97] for a survey). Courcelle [Cou90] proved a metatheorem, which easily implies numer...
Approximating cliquewidth and branchwidth
 JOURNAL OF COMBINATORIAL THEORY, SERIES B
, 2006
"... We construct a polynomialtime algorithm to approximate the branchwidth of certain symmetric submodular functions, and give two applications. The first is to graph “cliquewidth”. Cliquewidth is a measure of the difficulty of decomposing a graph in a kind of treestructure, and if a graph has cl ..."
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Cited by 57 (6 self)
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We construct a polynomialtime algorithm to approximate the branchwidth of certain symmetric submodular functions, and give two applications. The first is to graph “cliquewidth”. Cliquewidth is a measure of the difficulty of decomposing a graph in a kind of treestructure, and if a graph has cliquewidth at most k then the corresponding decomposition of the graph is called a “kexpression”. We find (for fixed k) an O(n 9 log n)time algorithm that, with input an nvertex graph, outputs either a (2 3k+2 − 1)expression for the graph, or a true statement that the graph has cliquewidth at least k + 1. (The best earlier algorithm algorithm, by Johansson [13], constructed a k log nexpression for graphs of cliquewidth at most k.) It was already known that several graph problems, NPhard on general graphs, are solvable in polynomial time if the input graph comes equipped with a kexpression (for fixed k). As a consequence of our algorithm, the same conclusion follows under the weaker hypothesis that the input graph has cliquewidth at most k (thus, we no longer need to be provided with an explicit kexpression). Another application is to the area of matroid branchwidth. For fixed k, we find an O(n 4)time algorithm that, with input an nelement matroid in terms of its rank oracle, either outputs a branchdecomposition of width at most 3k − 1 or a true statement that the matroid has branchwidth at least k + 1. The previous algorithm by Hliněn´y [11] was only for representable matroids.
Proximity search in databases
 In VLDB
, 1998
"... An information retrieval (IR) engine can rank documents based on textual proximityofkeywords within each document. In this paper we apply this notion to search across an entire database for objects that are \near " other relevant objects. Proximity search enables simple \focusing " queries ..."
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Cited by 56 (1 self)
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An information retrieval (IR) engine can rank documents based on textual proximityofkeywords within each document. In this paper we apply this notion to search across an entire database for objects that are \near " other relevant objects. Proximity search enables simple \focusing " queries based on general relationships among objects, helpful for interactive query sessions. We view the database as a graph, with data in vertices (objects) and relationships indicated by edges. Proximity is dened based on shortest paths between objects. We have implemented a prototype search engine that uses this model to enable keyword searches over databases, and we have found it very e ective for quickly nding relevant information. Computing the distance between objects in a graph stored on disk can be very expensive. Hence, we show how to build compact indexes that allow us to quickly nd the distance between objects at search time. Experiments show that our algorithms are ecient and scale well. 1
A simpler linear time algorithm for embedding graphs into an arbitrary surface and the genus of graphs of bounded treewidth
, 2008
"... ..."
Thin Junction Trees
 Advances in Neural Information Processing Systems 14
, 2001
"... We present an algorithm that induces a class of models with thin junction treesmodels that are characterized by an upper bound on the size of the maximal cliques of their triangulated graph. By ensuring that the junction tree is thin, inference in our models remains tractable throughout the l ..."
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Cited by 45 (1 self)
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We present an algorithm that induces a class of models with thin junction treesmodels that are characterized by an upper bound on the size of the maximal cliques of their triangulated graph. By ensuring that the junction tree is thin, inference in our models remains tractable throughout the learning process. This allows both an efficient implementation of an iterative scaling parameter estimation algorithm and also ensures that inference can be performed efficiently with the final model. We illustrate the approach with applications in handwritten digit recognition and DNA splice site detection.
Constraint Satisfaction, Bounded Treewidth, and FiniteVariable Logics
, 2002
"... We systematically investigate the connections between constraint satisfaction problems, structures of bounded treewidth, and definability in logics with a finite number of variables. We first show that constraint satisfaction problems on inputs of treewidth less than k are definable using Datalog ..."
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Cited by 44 (9 self)
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We systematically investigate the connections between constraint satisfaction problems, structures of bounded treewidth, and definability in logics with a finite number of variables. We first show that constraint satisfaction problems on inputs of treewidth less than k are definable using Datalog programs with at most k variables; this provides a new explanation for the tractability of these classes of problems. After this, we investigate constraint satisfaction on inputs that are homomorphically equivalent to structures of bounded treewidth.