In this paper, we define some new homomorphism-monotone parameters for hypergraphs. Using these parameters, we extend some graph homomorphism results to hypergraph case. Also, we present some bounds for some well-known invariants of hypergraphs such as fractional chromatic number,independent numer and some other invariants of hyergraphs, in terms of these parameters.

We determine under which conditions certain natural models of random constraint satisfaction problems have sharp thresholds of satisfiability. These models include graph and hypergraph homomorphism, the (d, k, t)-model, and binary constraint satisfaction problems with domain size 3.

We study non-uniform constraint satisfaction problems definable in monadic Datalog stratified by the use of non-linearity. We show how such problems can be described in terms of homomorphism dualities involving trees of bounded pathwidth and in algebraic terms. For this, we introduce a new parameter for trees that closely approximates pathwidth and can be characterised via a hypergraph searchin...

Structural decomposition methods have been developed for identifying tractable classes of instances of fundamental problems in databases, such as conjunctive queries and query containment, of the constraint satisfaction problem in artificial intelligence, or more generally of the homomorphism problem over relational structures. These methods work on the hypergraph structure of problem instances...

Complex networks are pervasive in the real world, capturing dyadic interactions between pairs of vertices, and a large corpus has emerged on their mining modeling. However, many phenomena comprised polyadic more than two vertices. Such complex hypergraphs range from emails among groups individuals, scholarly collaboration, or joint proteins living cells. models form an emergent topic, requiring...

Diagram editors which are tailored to a specific diagram language typically support either syntax-directed editing or free-hand editing, i.e., the user is either restricted to a collection of predefined editing operations, or he is not restricted at all, but misses the convenience of such complex editing operations. This paper proposes a concept for incorporating both modes into one editor in o...

Diagrams that serve as a visual input facility for programming environments have to be translated into some kind of semantic description. This paper describes such a method which is based on a specification of the translation process. The translation process starts with a diagram, which is simply represented as a collection of atomic diagram components, and it ends up with some data structure a...

A new approach to translating between natural language expressions and hypergraph-based semantic knowledge representations is proposed. Language comprehension is formulated in terms of homomorphisms mapping syntactic parse trees into semantic hypergraphs, and language generation as constraint satisfaction based on constraints derived via applying the inverse relations of these homomorphisms. Th...

Ahlswede and Winter [IEEE Trans. Inf. Th. 2002] introduced a Chernoff bound for matrix-valued random variables, which is a non-trivial generalization of the usual Chernoff bound for real-valued random variables. We present an efficient derandomization of their bound using the method of pessimistic estimators (see Raghavan [JCSS 1988]). As a consequence, we derandomize an efficient construction ...