K-way hypergraph partitioning has an ever-growing use in parallelization of scientific computing applications. We claim that hypergraph partitioning with multiple constraints and fixed vertices should be implemented using direct K-way refinement, instead of the widely adopted recursive bisection paradigm. Our arguments are based on the fact that recursive-bisection-based partitioning algorithms...

Alon, Kleitman, Lipton, Meshulam, Rabin and Spencer (Graphs. Combin. 7 (1991), no. 2, 97-99) proved, that for any hypergraph F = fF1; F2; : : : ; Fd(q 1)+1g, where q is a primepower, and d denotes the maximal degree of the hypergraph, there exists an F0 F , such that jSF2F0 F j 0 (mod q). We give a direct, alternative proof for this theorem, and we also give an explicit construction of a hyperg...

In this paper we consider the problem of determining all values of v for which there exists a decomposition of the complete 3-uniform hypergraph on v vertices into edge-disjoint copies of a given 3-uniform hypergraph. We solve the problem for each 3-uniform hypergraph having at most three edges and at most six vertices, and for the 3-uniform hypergraph of order 6 whose edges form the lines of t...

The paper considers the problem of computing a maximal independent set in a hypergraph (see 3] and 7]). We present an eecient deterministic NC algorithm for nding a maximal independent set in a hypergraph of dimension 3: the algorithm runs in time O(log 4 n) time on n + m processors of an EREW PRAM and is optimal up to a polylogarithmic factor. Our algorithm adapts the technique of Goldberg and...

1 Abstract A random greedy algorithm, somewhat modiied, is analyzed by using a real time context and showing that the variables remain close to the solution of a natural diierential equation. Given a (k + 1)-uniform simple hypergraph on N vertices, regular of degree D, the algorithm gives a packing of disjoint hyperedges containing all but O(ND ?1=k ln c D) of the vertices. Let H = (V; E) be a ...

3D object classification with multi-view representation has become very popular, thanks to the progress on computer techniques and graphic hardware, and attracted much research attention in recent years. Regarding this task, there are mainly two challenging issues, i.e., the complex correlation among multiple views and the possible imbalance data issue. In this work, we propose to employ the hy...

Multilevel partitioning methods that are inspired by principles of multiscaling are the most powerful practical hypergraph partitioning solvers. Hypergraph partitioning has many applications in disciplines ranging from scientific computing to data science. In this paper we introduce the concept of algebraic distance on hypergraphs and demonstrate its use as an algorithmic component in the coars...

The quality of the image plays a vital role in image processing technique. It can be determined by the removal of the noisy pixels in the images. In this paper, we designed the hypergraph model for the representation of images. We use noise removal algorithm for digital images.This algorithm is based on the hypergraph model of images. This is used to detect the noisy pixels and thus can be remo...

In this paper, we present a new hypergraph partitioning algorithm that is based on the multilevel paradigm. In the multilevel paradigm, a sequence of successively coarser hypergraphs is constructed. A bisection of the smallest hypergraph is computed and it is used to obtain a bisection of the original hypergraph by successively projecting and refining the bisection to the next level finer hyper...

The study of extremal problems related to independent sets in hypergraphs is a problem that has generated much interest. While independent sets in graphs are defined as sets of vertices containing no edges, hypergraphs have different types of independent sets depending on the number of vertices from an independent set allowed in an edge. We say that a subset of vertices is jindependent if its i...