Search results for " Hypergraphs"

showing 2 items of 2 documents

In the Shadows of a hypergraph: looking for associated primes of powers of squarefree monomial ideals

2018

The aim of this paper is to study the associated primes of powers of square-free monomial ideals. Each square-free monomial ideal corresponds uniquely to a finite simple hypergraph via the cover ideal construction, and vice versa. Let H be a finite simple hypergraph and J(H) the cover ideal of H. We define the shadows of hypergraph, H, described as a collection of smaller hypergraphs related to H under some conditions. We then investigate how the shadows of H preserve information about the associated primes of the powers of J(H). Finally, we apply our findings on shadows to study the persistence property of square-free monomial ideals and construct some examples exhibiting failure of contai…

HypergraphMonomialProperty (philosophy)Associated primes Cover ideals Hypergraphs Powers of idealsMathematics::Number Theory0102 computer and information sciencesHypergraphsCommutative Algebra (math.AC)01 natural sciencesCover idealsCombinatoricsSimple (abstract algebra)FOS: MathematicsMathematics - CombinatoricsDiscrete Mathematics and CombinatoricsPowers of ideals0101 mathematicsMathematicsAlgebra and Number TheoryIdeal (set theory)Mathematics::Commutative Algebra010102 general mathematicsAssociated primes; Cover ideals; Hypergraphs; Powers of idealsMonomial idealSquare-free integerMathematics - Commutative AlgebraSettore MAT/02 - AlgebraCover (topology)010201 computation theory & mathematicsAssociated primesSettore MAT/03 - GeometriaCombinatorics (math.CO)05C65 13F55 05E99 13C99
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Social Influence Maximization in Hypergraphs

2021

This work deals with a generalization of the minimum Target Set Selection (TSS) problem, a key algorithmic question in information diffusion research due to its potential commercial value. Firstly proposed by Kempe et al., the TSS problem is based on a linear threshold diffusion model defined on an input graph with node thresholds, quantifying the hardness to influence each node. The goal is to find the smaller set of items that can influence the whole network according to the diffusion model defined. This study generalizes the TSS problem on networks characterized by many-to-many relationships modeled via hypergraphs. Specifically, we introduce a linear threshold diffusion process on such …

Hypergraphsocial networksSelection (relational algebra)Computer scienceGeneralizationScienceQC1-999hypergraphGeneral Physics and Astronomy02 engineering and technologyAstrophysicsArticlehigh-order networkSet (abstract data type)influence diffusion020204 information systems0202 electrical engineering electronic engineering information engineeringDiscrete mathematicshigh-order networks; hypergraphs; influence diffusion; social networks; target set selectionPhysicsQMaximizationQB460-466high-order networkshypergraphstarget set selectionGraph (abstract data type)020201 artificial intelligence & image processingNode (circuits)Heuristics
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