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18
Discovering All Most Specific Sentences
 ACM Transactions on Database Systems
, 2003
"... this article, we show how the problems of finding frequent sets in relations and of finding minimal keys in databases can be reduced to this formulation. Using this theory extraction formulation [Mannila 1995, 1996; Mannila and Toivonen 1997], one can formulate general results about the complexity o ..."
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Cited by 73 (4 self)
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this article, we show how the problems of finding frequent sets in relations and of finding minimal keys in databases can be reduced to this formulation. Using this theory extraction formulation [Mannila 1995, 1996; Mannila and Toivonen 1997], one can formulate general results about the complexity of algorithms for these data mining tasks
Algorithms for Computing Minimal Unsatisfiable Subsets of Constraints
"... Abstract. Much research in the area of constraint processing has recently been focused on extracting small unsatisfiable “cores ” from unsatisfiable constraint systems with the goal of finding minimal unsatisfiable subsets (MUSes). While most techniques have provided ways to find an approximation of ..."
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Cited by 68 (9 self)
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Abstract. Much research in the area of constraint processing has recently been focused on extracting small unsatisfiable “cores ” from unsatisfiable constraint systems with the goal of finding minimal unsatisfiable subsets (MUSes). While most techniques have provided ways to find an approximation of an MUS (not necessarily minimal), we have developed a sound and complete algorithm for producing all MUSes of an unsatisfiable constraint system. In this paper, we describe a useful relationship between satisfiable and unsatisfiable subsets of constraints that we subsequently use as the foundation for MUS extraction algorithms, implemented for Boolean satisfiability constraints. The algorithms provide a framework with which many related subproblems can be solved, including relaxations of completeness to handle intractable instances, and we develop several variations of the basic algorithms to illustrate this. Experimental results demonstrate the performance of our algorithms, showing how the base algorithms run quickly on many instances, while the variations are valuable for producing results on instances whose complete results are intractably large. Furthermore, our algorithms are shown to perform better than the existing algorithms for solving either of the two distinct phases of our approach. 1.
Computing Simplicial Homology Based on Efficient Smith Normal Form Algorithms
, 2002
"... We recall that the calculation of homology with integer coecients of a simplicial complex reduces to the calculation of the Smith Normal Form of the boundary matrices which in general are sparse. We provide a review of several algorithms for the calculation of Smith Normal Form of sparse matrices an ..."
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Cited by 37 (2 self)
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We recall that the calculation of homology with integer coecients of a simplicial complex reduces to the calculation of the Smith Normal Form of the boundary matrices which in general are sparse. We provide a review of several algorithms for the calculation of Smith Normal Form of sparse matrices and compare their running times for actual boundary matrices. Then we describe alternative approaches to the calculation of simplicial homology. The last section then describes motivating examples and actual experiments with the GAP package that was implemented by the authors. These examples also include as an example of other homology theories some calculations of Lie algebra homology.
Generating All Maximal Models of a Boolean Expression
, 1999
"... We examine the computational problem of generating all maximal models of a Boolean expression in CNF. We give a resolutionlike method that reduces the unnegated variables of an expression while preserving its set of maximal models. We present an outputpolynomial algorithm for the 2CNF case and we ..."
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Cited by 28 (7 self)
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We examine the computational problem of generating all maximal models of a Boolean expression in CNF. We give a resolutionlike method that reduces the unnegated variables of an expression while preserving its set of maximal models. We present an outputpolynomial algorithm for the 2CNF case and we show that the problem cannot be solved in outputpolynomial time in the case of Horn expressions, unless P=NP, despite an affinity of this case to the recently subexponentially solved transversal hypergraph problem. The problem is of course trivial for 1valid and antiHorn expressions, and open for exclusiveors; it is NPhard in all other cases.
An Efficient Implementation of a Quasipolynomial Algorithm for Generating Hypergraph Transversals
, 2003
"... Given a finite set V, and a hypergraph H â 2V, the hypergraph transversal problem calls for enumerating all minimal hitting sets (transversals) for H. This problem plays an important role in practical applications as many other problems were shown to be polynomially equivalent to it. Fredman and ..."
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Cited by 18 (2 self)
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Given a finite set V, and a hypergraph H â 2V, the hypergraph transversal problem calls for enumerating all minimal hitting sets (transversals) for H. This problem plays an important role in practical applications as many other problems were shown to be polynomially equivalent to it. Fredman and Khachiyan (1996) gave an incremental quasipolynomial time algorithm for solving the hypergraph transversal problem [9]. In this paper, we present an efficient implementation of this algorithm. While we show that our implementation achieves the same bound on the running time as in [9], practical experience with this implementation shows that it can be substantially faster. We also show that a slight modification of the algorithm in [9] can be used to give a stronger bound on the running time.
An efficient algorithm for the transversal hypergraph generation
 Journal of Graph Algorithms and Applications
"... The Transversal Hypergraph Generation is the problem of generating, given a hypergraph, the set of its minimal transversals, i.e., the hypergraph whose hyperedges are the minimal hitting sets of the given one. The purpose of this paper is to present an efficient and practical algorithm for solving t ..."
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Cited by 18 (0 self)
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The Transversal Hypergraph Generation is the problem of generating, given a hypergraph, the set of its minimal transversals, i.e., the hypergraph whose hyperedges are the minimal hitting sets of the given one. The purpose of this paper is to present an efficient and practical algorithm for solving this problem. We show that the proposed algorithm operates in a way that rules out regeneration and, thus, its memory requirements are polynomially bounded to the size of the input hypergraph. Although no time bound for the algorithm is given, experimental evaluation and comparison with other approaches have shown that it behaves well in practice and it can successfully handle large problem instances.
Exact Algorithms for Finding Minimum Transversals in Rank3 Hypergraphs
, 2003
"... We present two algorithms for the problem of finding a minimum transversal in a hypergraph of rank 3, also known as the 3Hitting Set problem. This problem... ..."
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Cited by 8 (0 self)
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We present two algorithms for the problem of finding a minimum transversal in a hypergraph of rank 3, also known as the 3Hitting Set problem. This problem...
ABS: Adaptive Borders Search of frequent itemsets
"... In this paper, we present an ongoing work to discover maximal frequent itemsets in a transactional database. We propose an algorithm called ABS for Adaptive Borders Search, which is in the spirit of algorithms based on the concept of dualization. From an abstract point of view, our contribution can ..."
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In this paper, we present an ongoing work to discover maximal frequent itemsets in a transactional database. We propose an algorithm called ABS for Adaptive Borders Search, which is in the spirit of algorithms based on the concept of dualization. From an abstract point of view, our contribution can be seen as an improvement of the basic APRIORI algorithm for mining maximal frequent itemsets. The key point is to decide dynamically at which iteration, if any, the dualization has to be made to avoid the enumeration of all subsets of large maximal itemsets. Once the first dualization has been done from the current negative border, APRIORI is no longer used and instead, another dualization is carried out from the positive border known so far. The process is repeated until no change occurs anymore in the positive border in construction. Experiments have been done on FIMI datasets from which tradeoffs on adaptive behavior have been proposed to guess the best iteration for the first dualization. Far from being the best implementation wrt FIMI’03 contributions, performance evaluations of ABS exhibit better performance than IBE, the only public implementation based on the concept of dualization. 1
Trace Spaces: an Efficient New Technique for StateSpace Reduction
"... Abstract. Statespace reduction techniques, used primarily in modelcheckers, all rely on the idea that some actions are independent, hence could be taken in any (respective) order while put in parallel, without changing the semantics. It is thus not necessary to consider all execution paths in the ..."
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Abstract. Statespace reduction techniques, used primarily in modelcheckers, all rely on the idea that some actions are independent, hence could be taken in any (respective) order while put in parallel, without changing the semantics. It is thus not necessary to consider all execution paths in the interleaving semantics of a concurrent program, but rather some equivalence classes. The purpose of this paper is to describe a new algorithm to compute such equivalence classes, and a representative per class, which is based on ideas originating in algebraic topology. We introduce a geometric semantics of concurrent languages, where programs are interpreted as directed topological spaces, and study its properties in order to devise an algorithm for computing dihomotopy classes of execution paths. In particular, our algorithm is able to compute a controlflow graph for concurrent programs, possibly containing loops, which is “as reduced as possible ” in the sense that it generates traces modulo equivalence. A preliminary implementation was achieved, showing promising results towards efficient methods to analyze concurrent programs, with very promising results compared to partialorder reduction techniques.