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A New Algorithm for the Hypergraph Transversal Problem
, 2005
"... We consider the problem of finding all minimal transversals of a hypergraph H ⊆ 2 V, given by an explicit list of its hyperedges. We give a new decomposition technique for solving the problem with the following advantages: (i) Global parallelism: for certain classes of hypergraphs, e.g. hypergraphs ..."
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Cited by 4 (1 self)
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We consider the problem of finding all minimal transversals of a hypergraph H ⊆ 2 V, given by an explicit list of its hyperedges. We give a new decomposition technique for solving the problem with the following advantages: (i) Global parallelism: for certain classes of hypergraphs, e
Data mining, hypergraph transversals, and machine learning
, 1997
"... Several data mining problems can be formulated as problems of finding maximally specific sentences that are interesting in a database. We first show that this problem has a close relationship with the hypergraph transversal problem. We then analyze two algorithms that have been previously used in da ..."
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Cited by 77 (4 self)
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Several data mining problems can be formulated as problems of finding maximally specific sentences that are interesting in a database. We first show that this problem has a close relationship with the hypergraph transversal problem. We then analyze two algorithms that have been previously used
Cluster Ensembles  A Knowledge Reuse Framework for Combining Multiple Partitions
 Journal of Machine Learning Research
, 2002
"... This paper introduces the problem of combining multiple partitionings of a set of objects into a single consolidated clustering without accessing the features or algorithms that determined these partitionings. We first identify several application scenarios for the resultant 'knowledge reuse&ap ..."
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Cited by 603 (20 self)
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This paper introduces the problem of combining multiple partitionings of a set of objects into a single consolidated clustering without accessing the features or algorithms that determined these partitionings. We first identify several application scenarios for the resultant 'knowledge reuse
Identifying the minimal transversals of a hypergraph and related problems
 SIAM Journal on Computing
, 1995
"... The paper considers two decision problems on hypergraphs, hypergraph saturation and recognition of the transversal hypergraph, and discusses their significance for several search problems in applied computer science. Hypergraph saturation, i.e., given a hypergraph H, decide if every subset of vertic ..."
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Cited by 155 (8 self)
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The paper considers two decision problems on hypergraphs, hypergraph saturation and recognition of the transversal hypergraph, and discusses their significance for several search problems in applied computer science. Hypergraph saturation, i.e., given a hypergraph H, decide if every subset
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
Transversal Numbers of Uniform Hypergraphs
 GRAPHS AND COMBINATORICS
, 1990
"... The transversal number ~(H) of a hypergraph H is the minimum eardinality of a set of vertices that intersects all edges of H. For k ~ 1 define ck = supz(H)/(ra + n), where H ranges over all kuniform hypergraphs with n vertices and m edges. Applying probabilistic arguments we show that ck = (1 + o ..."
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Cited by 45 (3 self)
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The transversal number ~(H) of a hypergraph H is the minimum eardinality of a set of vertices that intersects all edges of H. For k ~ 1 define ck = supz(H)/(ra + n), where H ranges over all kuniform hypergraphs with n vertices and m edges. Applying probabilistic arguments we show that ck = (1
Levelwise Search and Borders of Theories in Knowledge Discovery
, 1997
"... One of the basic problems in knowledge discovery in databases (KDD) is the following: given a data set r, a class L of sentences for defining subgroups of r, and a selection predicate, find all sentences of L deemed interesting by the selection predicate. We analyze the simple levelwise algorithm fo ..."
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Cited by 263 (15 self)
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process: given r and a set of sentences S ` L, determine whether S is exactly the set of interesting statements about r. We show strong connections between the verification problem and the hypergraph transversal problem. The verification problem arises in a natural way when using sampling to speed up
PROBLEMS AND RESULTS ON 3CHROMATIC HYPERGRAPHS AND SOME RELATED QUESTIONS
 COLLOQUIA MATHEMATICA SOCIETATIS JANOS BOLYAI 10. INFINITE AND FINITE SETS, KESZTHELY (HUNGARY)
, 1973
"... A hypergraph is a collection of sets. This paper deals with finite hypergraphs only. The sets in the hypergraph are called edges, the elements of these edges are points. The degree of a point is the number of edges containing it. The hypergraph is runiform if every edge has r points. A hypergraph i ..."
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Cited by 311 (0 self)
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A hypergraph is a collection of sets. This paper deals with finite hypergraphs only. The sets in the hypergraph are called edges, the elements of these edges are points. The degree of a point is the number of edges containing it. The hypergraph is runiform if every edge has r points. A hypergraph
Evaluation of an Algorithm for the Transversal Hypergraph Problem
 In Algorithm Engineering
, 1999
"... The Transversal Hypergraph Problem is the problem of computing, given a hypergraph, the set of its minimal transversals, i.e. the hypergraph whose hyperedges are all minimal hitting sets of the given one. This problem turns out to be central in various fields of Computer Science. We present and ..."
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Cited by 18 (5 self)
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The Transversal Hypergraph Problem is the problem of computing, given a hypergraph, the set of its minimal transversals, i.e. the hypergraph whose hyperedges are all minimal hitting sets of the given one. This problem turns out to be central in various fields of Computer Science. We present
Coupons collecting and transversals of hypergraphs
"... The classic CouponCollector Problem (CCP) is generalized. Only basic probability theory is used. Centerpiece rather is an algorithm that efficiently counts all kelement transversals of a set system. ..."
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Cited by 1 (1 self)
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The classic CouponCollector Problem (CCP) is generalized. Only basic probability theory is used. Centerpiece rather is an algorithm that efficiently counts all kelement transversals of a set system.
Results 1  10
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