Recent developments in approximate counting have made startling progress developing fast algorithmic methods for approximating the number of solutions to constraint satisfaction problems (CSPs) with large arities, using connections Lovász Local Lemma. Nevertheless, boundaries these CSPs non-Boolean domain are not well-understood. Our goal this article is fill gap and obtain strong inapproximabi...

Abstract In this chapter, the applications of hypergraph computation in computer vision are introduced. Computer is one most widely used areas computation. The hypergraphs can be constructed by modeling high-order relationship among inter- or intra-visual samples, and then tasks solved procedures. More specifically, four typical applications, including visual classification, 3D object retrieval...

A relation on a hypergraph is a binary relation on the set consisting of the nodes and hyperedges together, and which satisfies a constraint involving the incidence structure of the hypergraph. These relations correspond to join-preserving mappings on the lattice of subhypergraphs. This paper studies the algebra of these relations, in particular the analogues of the familiar operations of compl...

In this paper, we show that the eigenvectors associated with the zero eigenvalues of the Laplacian and signless Lapacian tensors of a k-uniform hypergraph are closely related to some configured components of that hypergraph. We show that the components of an eigenvector associated with the zero eigenvalue of the Laplacian or signless Lapacian tensor have the same modulus. Moreover, under a cano...

An [n, k, r]-hypergraph is a hypergraph :Yf = (V, E) whose vertex set V is partitioned into n k-element sets V1, V2, ... , Vn and for which, for each choice of r indices, 1 :::;; i1 < i2 < ... < ir :::;; n, there is exactly one edge e E E such that len Vii = 1 if i E {i1, i2, ... , ir} and otherwise le n Vii = 0. An independent transversal of an [n, k, r ]-hypergraph is a set T = {a1,a2, .. . ,...