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Coverings and Matchings in rPartite Hypergraphs
, 2010
"... Ryser’s conjecture postulates that, for rpartite hypergraphs, τ ≤ (r − 1)ν where τ is the covering number of the hypergraph and ν is the matching number. Although this conjecture has been open since the 1960’s, researchers have resolved it for special cases such as for intersecting hypergraphs wher ..."
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Ryser’s conjecture postulates that, for rpartite hypergraphs, τ ≤ (r − 1)ν where τ is the covering number of the hypergraph and ν is the matching number. Although this conjecture has been open since the 1960’s, researchers have resolved it for special cases such as for intersecting hypergraphs
Cores of Random rPartite Hypergraphs
, 2010
"... We show that the threshold cr,k for appearance of a kcore in a random rpartite runiform hypergraph Gr,n,m is the same as for a random runiform hypergraph with cn/r edges without the rpartite restriction, where r, k≥2. In both cases, the average degree is c. This is an important problem in the a ..."
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Cited by 3 (2 self)
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We show that the threshold cr,k for appearance of a kcore in a random rpartite runiform hypergraph Gr,n,m is the same as for a random runiform hypergraph with cn/r edges without the rpartite restriction, where r, k≥2. In both cases, the average degree is c. This is an important problem
On a Theorem of Lovász on Covers in rpartite Hypergraphs
 Combinatorica
, 1996
"... A theorem of Lovasz asserts that (H)= (H) r=2 for every rpartite hypergraph H (where and denote the covering number and fractional covering number respectively). Here it is shown that the same upper bound is valid for a more general class of hypergraphs: those which admit a partition (V ..."
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Cited by 7 (2 self)
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A theorem of Lovasz asserts that (H)= (H) r=2 for every rpartite hypergraph H (where and denote the covering number and fractional covering number respectively). Here it is shown that the same upper bound is valid for a more general class of hypergraphs: those which admit a partition (V
Rainbow matchings in rpartite rgraphs
"... Given a collection of matchings M = (M1,M2,...,Mq) (repetitions allowed), a matching M contained in ⋃ M is said to be srainbow for M if it contains representatives from s matchings Mi (where each edge is allowed to represent just one Mi). Formally, this means that there is a function φ: M → [q] suc ..."
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Cited by 2 (0 self)
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] such that e ∈ M φ(e) for all e ∈ M, and Im(φ)  � s. Let f(r,s,t) be the maximal k for which there exists a set of k matchings of size t in some rpartite hypergraph, such that there is no srainbow matching of size t. We prove that f(r,s,t) � 2 r−1 (s − 1), make the conjecture that equality holds for all
Graphical models, exponential families, and variational inference
, 2008
"... The formalism of probabilistic graphical models provides a unifying framework for capturing complex dependencies among random variables, and building largescale multivariate statistical models. Graphical models have become a focus of research in many statistical, computational and mathematical fiel ..."
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Cited by 800 (26 self)
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The formalism of probabilistic graphical models provides a unifying framework for capturing complex dependencies among random variables, and building largescale multivariate statistical models. Graphical models have become a focus of research in many statistical, computational and mathematical fields, including bioinformatics, communication theory, statistical physics, combinatorial optimization, signal and image processing, information retrieval and statistical machine learning. Many problems that arise in specific instances — including the key problems of computing marginals and modes of probability distributions — are best studied in the general setting. Working with exponential family representations, and exploiting the conjugate duality between the cumulant function and the entropy for exponential families, we develop general variational representations of the problems of computing likelihoods, marginal probabilities and most probable configurations. We describe how a wide varietyof algorithms — among them sumproduct, cluster variational methods, expectationpropagation, mean field methods, maxproduct and linear programming relaxation, as well as conic programming relaxations — can all be understood in terms of exact or approximate forms of these variational representations. The variational approach provides a complementary alternative to Markov chain Monte Carlo as a general source of approximation methods for inference in largescale statistical models.
Community detection in graphs
, 2009
"... The modern science of networks has brought significant advances to our understanding of complex systems. One of the most relevant features of graphs representing real systems is community structure, or clustering, i. e. the organization of vertices in clusters, with many edges joining vertices of th ..."
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Cited by 801 (1 self)
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The modern science of networks has brought significant advances to our understanding of complex systems. One of the most relevant features of graphs representing real systems is community structure, or clustering, i. e. the organization of vertices in clusters, with many edges joining vertices of the same cluster and comparatively few edges joining vertices of different clusters. Such
New Algorithms for Fast Discovery of Association Rules
 In 3rd Intl. Conf. on Knowledge Discovery and Data Mining
, 1997
"... Association rule discovery has emerged as an important problem in knowledge discovery and data mining. The association mining task consists of identifying the frequent itemsets, and then forming conditional implication rules among them. In this paper we present efficient algorithms for the discovery ..."
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Cited by 391 (26 self)
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Association rule discovery has emerged as an important problem in knowledge discovery and data mining. The association mining task consists of identifying the frequent itemsets, and then forming conditional implication rules among them. In this paper we present efficient algorithms for the discovery of frequent itemsets, which forms the compute intensive phase of the task. The algorithms utilize the structural properties of frequent itemsets to facilitate fast discovery. The related database items are grouped together into clusters representing the potential maximal frequent itemsets in the database. Each cluster induces a sublattice of the itemset lattice. Efficient lattice traversal techniques are presented, which quickly identify all the true maximal frequent itemsets, and all their subsets if desired. We also present the effect of using different database layout schemes combined with the proposed clustering and traversal techniques. The proposed algorithms scan a (preprocessed) d...
On Perfect Matchings in Uniform Hypergraphs with . . .
, 2009
"... We study sufficient ℓdegree (1 ≤ ℓ < k) conditions for the appearance of perfect and nearly perfect matchings in kuniform hypergraphs. In particular, we obtain a minimum vertex degree condition (ℓ = 1) for 3uniform hypergraphs, which is approximately tight, by showing that every 3uniform hyp ..."
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Cited by 29 (4 self)
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We study sufficient ℓdegree (1 ≤ ℓ < k) conditions for the appearance of perfect and nearly perfect matchings in kuniform hypergraphs. In particular, we obtain a minimum vertex degree condition (ℓ = 1) for 3uniform hypergraphs, which is approximately tight, by showing that every 3uniform
Independence and Matchings in σhypergraphs
"... Let σ be a partition of the positive integer r. A σhypergraph H = H(n, r, qσ) is an runiform hypergraph on nq vertices which are partitioned into n classes V1, V2,..., Vn each containing q vertices. An rsubset K of vertices is an edge of the hypergraph if the partition of r formed by the nonze ..."
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Let σ be a partition of the positive integer r. A σhypergraph H = H(n, r, qσ) is an runiform hypergraph on nq vertices which are partitioned into n classes V1, V2,..., Vn each containing q vertices. An rsubset K of vertices is an edge of the hypergraph if the partition of r formed by the non
Results 1  10
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3,795