The existence of relational products in categories of relations is strongly connected with the representability of that category. In this paper we propose a canonical weakening of the notion of a relational product. Unlike the strong version any (small) category of relations can be embedded into a suitable category providing all weak relational products. Furthermore, we investigate the categori...

We study an extension of the DeGroot model where part of the players may be rebels. The updating rule for rebels is quite different with that of normal players (which are referred to as conformists): at each step a rebel first takes the opposite value of the weighted average of her neighbors’ opinions, i.e. 1 minus that average (the opinion space is assumed to be [0,1] as usual), and then updat...

We provide an efficient algorithm for computing the candidate keys of a relational database schema. The algorithm exploits the ‘arrangement’ of attributes in the functional dependencies to determine which attributes are essential and useful for determining the keys and which attributes should not be considered. A more generalized algorithm using attribute graphs is then provided which allows a ...

We characterize the graphs for which all 2-connected non-bipartite subgraphs have a strongly connected orientation in which each directed circuit has an odd number of edges. We also give a polynomial-time algorithm to find such an orientation in these graphs. Moreover, we give an algorithm that given any orientation of such a graph, determines if it has an even directed circuit. The proofs of t...

Result checking is a general methodology for ensuring that untrusted computations are valid. Its essence lies in defining efficient checking procedures to verify that a result satisfies some expected property. Result checking often relies on certificates to make the verification process efficient, and thus involves two strongly connected tasks: the generation of certificates and the implementat...

We consider problems to make a given bidirected graph strongly connected with minimum cardinality of additional signs or additional arcs. For the former problem, we show the minimum number of additional signs and give a linear-time algorithm for finding an optimal solution. For the latter problem, we give a linear-time algorithm for finding a feasible solution whose size is equal to the obvious...

An n-tournament is an orientation of a complete n-partite graph. It was proved by J.A. Bondy in 1976 that every strongly connected n-partite tournament has an n-cycle. We characterize strongly connected n-partite tournaments in which a longest cycle is of length n and, thus, settle a problem in L. Volkmann, Discrete Math. 245 (2002) 19-53.

The AllDifferent constraint is a crucial component of any constraint toolkit, language or solver, since it is very widely used in a variety of constraint models. The literature contains many different versions of this constraint, which trade strength of inference against computational cost. In this paper, we focus on the highest strength of inference, enforcing a property known as generalised a...

Minimal siphons in the class of S4 PR nets have become a conceptual and practical central tool for the study of the resource allocation related aspects in discrete event dynamic systems as, for example, the existence of deadlocks. Therefore the availability of efficient algorithms to compute the minimal siphons is essential. In this paper we try to take advantage of the particular properties of...