ÐIn this work, we show that the standard graph-partitioning-based decomposition of sparse matrices does not reflect the actual communication volume requirement for parallel matrix-vector multiplication. We propose two computational hypergraph models which avoid this crucial deficiency of the graph model. The proposed models reduce the decomposition problem to the well-known hypergraph partition...

We consider a generalization of the notion of transversal to a finite hypergraph, so called weighted transversals. Given a non-negative weight vector assigned to each hyperedge of the input hypergraph, we define a weighted transversal as a minimal vertex set which intersects a collection of hyperedges of sufficiently large total weight. We show that the hypergraph of all weighted transversals i...

This chapter explores original techniques for the construction of hypergraph models for computer vision applications. A hypergraph is a generalization of a pairwise simple graph, where an edge can connect any number of vertices. The expressive power of the hypergraph models places a special emphasis on the relationship among three or more objects, which has made hypergraphs better models of cho...

The cyclicity of a hypergraph is an efficiently computable integer that extends the notion of the cyclomatic number of a graph. Generalizing the notion of the degree of a node in a graph, we define the star articulation degree of a subedge in a hypergraph, and then use it to set up the expression for the cyclicity. The basic properties of cyclicity are that it is zero on acyclic hypergraphs and...

The theory of mixed hypergraph coloring was first introduced by Voloshin in 1993 and has been growing ever since. The proper coloring of a mixed hypergraph H = (X, C,D) is the coloring of the vertex set X so that no D-hyperedge is monochromatic and no C-hyperedge is polychromatic. A mixed hypergraph with hyperedges of type D, C or B is commonly known as a D, C, or B-hypergraph respectively wher...

Claude BERGE C.N.R.S., Paris The hypergraphs whose chromatic number is ~ 2 ("bicolorable" hypergraphs) were introduced by E.W. Miller [13] under the name of "set-systems with Property B". This concept appears in Number Theory (see [5], [10]). It is also useful for some problems in positional games and Operations Research (see [3], [4], [7]); different results have been found under the form of i...