The Experts below are selected from a list of 1150482 Experts worldwide ranked by ideXlab platform
Leonid Khachiyan - One of the best experts on this subject based on the ideXlab platform.
-
an efficient implementation of a quasi polynomial algorithm for generating hypergraph Transversals and its application in joint generation
Symposium on Discrete Algorithms, 2006Co-Authors: Leonid Khachiyan, Endre Boros, Khaled Elbassioni, Vladimir GurvichAbstract:Given a finite set V, and a hypergraph H ⊆ 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 [On the complexity of dualization of monotone disjunctive normal forms, J. Algorithms 21 (1996) 618-628] gave an incremental quasi-polynomial-time algorithm for solving the hypergraph transversal problem. In this paper, we present an efficient implementation of this algorithm. While we show that our implementation achieves the same theoretical worst-case bound, practical experience with this implementation shows that it can be substantially faster. We also show that a slight modification of the original algorithm can be used to obtain a stronger bound on the running time.More generally, we consider a monotone property π over a bounded n-dimensional integral box. As an important application of the above hypergraph transversal problem, pioneered by Bioch and Ibaraki [Complexity of identification and dualization of positive Boolean functions, Inform. and Comput. 123 (1995) 50-63], we consider the problem of incrementally generating simultaneously all minimal subsets satisfying π and all maximal subsets not satisfying π, for properties given by a polynomial-time satisfiability oracle. Problems of this type arise in many practical applications. It is known that the above joint generation problem can be solved in incremental quasi-polynomial time via a polynomial-time reduction to a generalization of the hypergraph transversal problem on integer boxes. In this paper we present an efficient implementation of this procedure, and present experimental results to evaluate our implementation for a number of interesting monotone properties π.
-
an efficient implementation of a quasi polynomial algorithm for generating hypergraph Transversals
European Symposium on Algorithms, 2003Co-Authors: Endre Boros, Vladimir Gurvich, Khaled Elbassioni, Leonid KhachiyanAbstract:Given a finite set V, and a hypergraph \(\mathcal{H} \subseteq 2^V\), the hypergraph transversal problem calls for enumerating all minimal hitting sets (Transversals) for \(\mathcal{H}\). 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 quasi-polynomial 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 implementation of a quasi polynomial algorithm for generating hypergraph Transversals
Lecture Notes in Computer Science, 2003Co-Authors: Endre Boros, Vladimir Gurvich, Khaled Elbassioni, Leonid KhachiyanAbstract:Given a finite set V, and a hypergraph H C 2 V , 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 quasi-polynomial 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.
-
dual bounded generating problems partial and multiple Transversals of a hypergraph
SIAM Journal on Computing, 2001Co-Authors: Endre Boros, Vladimir Gurvich, Leonid KhachiyanAbstract:We consider two generalizations of the notion of transversal to a finite hypergraph, the so-called multiple and partial Transversals. Multiple Transversals naturally arise in 0-1 programming, while partial Transversals are related to data mining and machine learning. We show that for an arbitrary hypergraph the families of multiple and partial Transversals are both dual-bounded in the sense that the size of the corresponding dual hypergraph is bounded by a polynomial in the cardinality and the length of description of the input hypergraph. Our bounds are based on new inequalities of extremal set theory and threshold Boolean logic, which may be of independent interest. We also show that the problems of generating all multiple and all partial Transversals for a given hypergraph are polynomial-time reducible to the generation of all ordinary Transversals for another hypergraph, i.e., to the well-known dualization problem for hypergraphs. As a corollary, we obtain incremental quasi-polynomial-time algorithms for both of the above problems, as well as for the generation of all the minimal binary solutions for an arbitrary monotone system of linear inequalities.
Vladimir Gurvich - One of the best experts on this subject based on the ideXlab platform.
-
an efficient implementation of a quasi polynomial algorithm for generating hypergraph Transversals and its application in joint generation
Symposium on Discrete Algorithms, 2006Co-Authors: Leonid Khachiyan, Endre Boros, Khaled Elbassioni, Vladimir GurvichAbstract:Given a finite set V, and a hypergraph H ⊆ 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 [On the complexity of dualization of monotone disjunctive normal forms, J. Algorithms 21 (1996) 618-628] gave an incremental quasi-polynomial-time algorithm for solving the hypergraph transversal problem. In this paper, we present an efficient implementation of this algorithm. While we show that our implementation achieves the same theoretical worst-case bound, practical experience with this implementation shows that it can be substantially faster. We also show that a slight modification of the original algorithm can be used to obtain a stronger bound on the running time.More generally, we consider a monotone property π over a bounded n-dimensional integral box. As an important application of the above hypergraph transversal problem, pioneered by Bioch and Ibaraki [Complexity of identification and dualization of positive Boolean functions, Inform. and Comput. 123 (1995) 50-63], we consider the problem of incrementally generating simultaneously all minimal subsets satisfying π and all maximal subsets not satisfying π, for properties given by a polynomial-time satisfiability oracle. Problems of this type arise in many practical applications. It is known that the above joint generation problem can be solved in incremental quasi-polynomial time via a polynomial-time reduction to a generalization of the hypergraph transversal problem on integer boxes. In this paper we present an efficient implementation of this procedure, and present experimental results to evaluate our implementation for a number of interesting monotone properties π.
-
an efficient implementation of a quasi polynomial algorithm for generating hypergraph Transversals
European Symposium on Algorithms, 2003Co-Authors: Endre Boros, Vladimir Gurvich, Khaled Elbassioni, Leonid KhachiyanAbstract:Given a finite set V, and a hypergraph \(\mathcal{H} \subseteq 2^V\), the hypergraph transversal problem calls for enumerating all minimal hitting sets (Transversals) for \(\mathcal{H}\). 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 quasi-polynomial 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 implementation of a quasi polynomial algorithm for generating hypergraph Transversals
Lecture Notes in Computer Science, 2003Co-Authors: Endre Boros, Vladimir Gurvich, Khaled Elbassioni, Leonid KhachiyanAbstract:Given a finite set V, and a hypergraph H C 2 V , 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 quasi-polynomial 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.
-
dual bounded generating problems partial and multiple Transversals of a hypergraph
SIAM Journal on Computing, 2001Co-Authors: Endre Boros, Vladimir Gurvich, Leonid KhachiyanAbstract:We consider two generalizations of the notion of transversal to a finite hypergraph, the so-called multiple and partial Transversals. Multiple Transversals naturally arise in 0-1 programming, while partial Transversals are related to data mining and machine learning. We show that for an arbitrary hypergraph the families of multiple and partial Transversals are both dual-bounded in the sense that the size of the corresponding dual hypergraph is bounded by a polynomial in the cardinality and the length of description of the input hypergraph. Our bounds are based on new inequalities of extremal set theory and threshold Boolean logic, which may be of independent interest. We also show that the problems of generating all multiple and all partial Transversals for a given hypergraph are polynomial-time reducible to the generation of all ordinary Transversals for another hypergraph, i.e., to the well-known dualization problem for hypergraphs. As a corollary, we obtain incremental quasi-polynomial-time algorithms for both of the above problems, as well as for the generation of all the minimal binary solutions for an arbitrary monotone system of linear inequalities.
Endre Boros - One of the best experts on this subject based on the ideXlab platform.
-
an efficient implementation of a quasi polynomial algorithm for generating hypergraph Transversals and its application in joint generation
Symposium on Discrete Algorithms, 2006Co-Authors: Leonid Khachiyan, Endre Boros, Khaled Elbassioni, Vladimir GurvichAbstract:Given a finite set V, and a hypergraph H ⊆ 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 [On the complexity of dualization of monotone disjunctive normal forms, J. Algorithms 21 (1996) 618-628] gave an incremental quasi-polynomial-time algorithm for solving the hypergraph transversal problem. In this paper, we present an efficient implementation of this algorithm. While we show that our implementation achieves the same theoretical worst-case bound, practical experience with this implementation shows that it can be substantially faster. We also show that a slight modification of the original algorithm can be used to obtain a stronger bound on the running time.More generally, we consider a monotone property π over a bounded n-dimensional integral box. As an important application of the above hypergraph transversal problem, pioneered by Bioch and Ibaraki [Complexity of identification and dualization of positive Boolean functions, Inform. and Comput. 123 (1995) 50-63], we consider the problem of incrementally generating simultaneously all minimal subsets satisfying π and all maximal subsets not satisfying π, for properties given by a polynomial-time satisfiability oracle. Problems of this type arise in many practical applications. It is known that the above joint generation problem can be solved in incremental quasi-polynomial time via a polynomial-time reduction to a generalization of the hypergraph transversal problem on integer boxes. In this paper we present an efficient implementation of this procedure, and present experimental results to evaluate our implementation for a number of interesting monotone properties π.
-
an efficient implementation of a quasi polynomial algorithm for generating hypergraph Transversals
European Symposium on Algorithms, 2003Co-Authors: Endre Boros, Vladimir Gurvich, Khaled Elbassioni, Leonid KhachiyanAbstract:Given a finite set V, and a hypergraph \(\mathcal{H} \subseteq 2^V\), the hypergraph transversal problem calls for enumerating all minimal hitting sets (Transversals) for \(\mathcal{H}\). 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 quasi-polynomial 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 implementation of a quasi polynomial algorithm for generating hypergraph Transversals
Lecture Notes in Computer Science, 2003Co-Authors: Endre Boros, Vladimir Gurvich, Khaled Elbassioni, Leonid KhachiyanAbstract:Given a finite set V, and a hypergraph H C 2 V , 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 quasi-polynomial 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.
-
dual bounded generating problems partial and multiple Transversals of a hypergraph
SIAM Journal on Computing, 2001Co-Authors: Endre Boros, Vladimir Gurvich, Leonid KhachiyanAbstract:We consider two generalizations of the notion of transversal to a finite hypergraph, the so-called multiple and partial Transversals. Multiple Transversals naturally arise in 0-1 programming, while partial Transversals are related to data mining and machine learning. We show that for an arbitrary hypergraph the families of multiple and partial Transversals are both dual-bounded in the sense that the size of the corresponding dual hypergraph is bounded by a polynomial in the cardinality and the length of description of the input hypergraph. Our bounds are based on new inequalities of extremal set theory and threshold Boolean logic, which may be of independent interest. We also show that the problems of generating all multiple and all partial Transversals for a given hypergraph are polynomial-time reducible to the generation of all ordinary Transversals for another hypergraph, i.e., to the well-known dualization problem for hypergraphs. As a corollary, we obtain incremental quasi-polynomial-time algorithms for both of the above problems, as well as for the generation of all the minimal binary solutions for an arbitrary monotone system of linear inequalities.
Ioan Marcut - One of the best experts on this subject based on the ideXlab platform.
-
normal forms for poisson maps and symplectic groupoids around poisson Transversals
Letters in Mathematical Physics, 2018Co-Authors: Pedro Frejlich, Ioan MarcutAbstract:Poisson Transversals are submanifolds in a Poisson manifold which intersect all symplectic leaves transversally and symplectically. In this communication, we prove a normal form theorem for Poisson maps around Poisson Transversals. A Poisson map pulls a Poisson transversal back to a Poisson transversal, and our first main result states that simultaneous normal forms exist around such Transversals, for which the Poisson map becomes transversally linear, and intertwines the normal form data of the Transversals. Our second result concerns symplectic integrations. We prove that a neighborhood of a Poisson transversal is integrable exactly when the Poisson transversal itself is integrable, and in that case we prove a normal form theorem for the symplectic groupoid around its restriction to the Poisson transversal, which puts all structure maps in normal form. We conclude by illustrating our results with examples arising from Lie algebras.
-
normal forms for poisson maps and symplectic groupoids around poisson Transversals
arXiv: Symplectic Geometry, 2015Co-Authors: Pedro Frejlich, Ioan MarcutAbstract:Poisson Transversals are those submanifolds in a Poisson manifold which intersect all symplectic leaves transversally and symplectically. In a previous note we proved a normal form theorem around such submanifolds. In this communication, we promote that result to a normal form theorem for Poisson maps around Poisson Transversals. A Poisson map pulls a Poisson transversal back to a Poisson transversal, and our first main result states that simultaneous normal forms exist around such Transversals, for which the Poisson map becomes transversally linear, and intertwines the normal form data of the Transversals. Our second main result concerns symplectic integrations. We prove that a neighborhood of a Poisson transversal is integrable exactly when the Poisson transversal itself is integrable, and in that case we prove a normal form theorem for the symplectic groupoid around its restriction to the Poisson transversal, which puts all its structure maps in normal form. We conclude the paper by illustrating our results with examples arising from Lie algebras.
Khaled Elbassioni - One of the best experts on this subject based on the ideXlab platform.
-
an efficient implementation of a quasi polynomial algorithm for generating hypergraph Transversals and its application in joint generation
Symposium on Discrete Algorithms, 2006Co-Authors: Leonid Khachiyan, Endre Boros, Khaled Elbassioni, Vladimir GurvichAbstract:Given a finite set V, and a hypergraph H ⊆ 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 [On the complexity of dualization of monotone disjunctive normal forms, J. Algorithms 21 (1996) 618-628] gave an incremental quasi-polynomial-time algorithm for solving the hypergraph transversal problem. In this paper, we present an efficient implementation of this algorithm. While we show that our implementation achieves the same theoretical worst-case bound, practical experience with this implementation shows that it can be substantially faster. We also show that a slight modification of the original algorithm can be used to obtain a stronger bound on the running time.More generally, we consider a monotone property π over a bounded n-dimensional integral box. As an important application of the above hypergraph transversal problem, pioneered by Bioch and Ibaraki [Complexity of identification and dualization of positive Boolean functions, Inform. and Comput. 123 (1995) 50-63], we consider the problem of incrementally generating simultaneously all minimal subsets satisfying π and all maximal subsets not satisfying π, for properties given by a polynomial-time satisfiability oracle. Problems of this type arise in many practical applications. It is known that the above joint generation problem can be solved in incremental quasi-polynomial time via a polynomial-time reduction to a generalization of the hypergraph transversal problem on integer boxes. In this paper we present an efficient implementation of this procedure, and present experimental results to evaluate our implementation for a number of interesting monotone properties π.
-
an efficient implementation of a quasi polynomial algorithm for generating hypergraph Transversals
European Symposium on Algorithms, 2003Co-Authors: Endre Boros, Vladimir Gurvich, Khaled Elbassioni, Leonid KhachiyanAbstract:Given a finite set V, and a hypergraph \(\mathcal{H} \subseteq 2^V\), the hypergraph transversal problem calls for enumerating all minimal hitting sets (Transversals) for \(\mathcal{H}\). 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 quasi-polynomial 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 implementation of a quasi polynomial algorithm for generating hypergraph Transversals
Lecture Notes in Computer Science, 2003Co-Authors: Endre Boros, Vladimir Gurvich, Khaled Elbassioni, Leonid KhachiyanAbstract:Given a finite set V, and a hypergraph H C 2 V , 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 quasi-polynomial 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.
