Vedecké časopisy a ročenky vydávané na pôde SAV

One of the fundamental tasks in any distributed computing system is routing messages between pairs of nodes. An Interval Routing Scheme (IRS) is a~space efficient way of routing messages in a network. The problem of characterizing graphs that support an IRS is a well-known problem and has been studied for some variants of IRS. It is natural to assume that the costs of links may vary over time (dynamic cost links) and to try to find an IRS which routes all messages on shortest paths (optimum IRS). In this paper, we study this problem for a~variant of IRS in which the labels assigned to the vertices are $d$-ary integer tuples ($d$-dimensional IRS). The only known results in this case are for specific graphs like hypercubes, $n$-dimensional grids, or for the 1-dimensional case. We give a complete characterization for the class of networks supporting multi-dimensional strict and linear (no cyclic intervals) interval routing schemes with dynamic cost links.

This paper presents an algorithm for two-level Boolean minimization (BOOM) based on a new implicant generation paradigm. In contrast to all previous minimization methods, where the implicants are generated bottom-up, the proposed method uses a top-down approach. Thus, instead of increasing the dimensionality of implicants by omitting literals from their terms, the dimension of a term is gradually decreased by adding new literals. The method is advantageous especially for functions with many input variables (up to thousands) and with only few care terms defined, where other minimization tools are not applicable because of the long runtime. The method has been tested on several different kinds of problems and the results were compared with ESPRESSO.

Cooperation among agents has been the object of many recently published papers. Cooperation might be formulated and work in many forms, between different kinds of agents and situations in which they are situated. In addition, it is also influenced a lot by the agent's intelligence, mutual relationships and the willingness to cooperate with other ones. The main focus of this paper is to solve the problem of how to create optimal coalitions of the given agents with the purpose to improve the collective performance. The coalition is a possible form of cooperation in which the common goal has the highest priority for all members included in it. Further, we introduce methods for finding the sub-optimal solutions, which are able to approximate the range of the optimal solutions. Finally we discuss the problem of creating coalition with more parameters.

It is well known that there does not exist a Boolean function f: Z_2^m ightarrow Z_2^n satisfying both basic cryptologic criteria, balancedness and perfect nonlinearity. In /9/ it was shown that, if we use as a domain quasigroup G instead of the group Z_2^n, one can find functions which are at the same time balanced and perfectly nonlinear. Such functions have completely flat difference table. We continue in our previous work, but we turn our attention to the worst case when all lines of Cayley table of G define so called linear structure of f (/5/). We solve this problem in both directions: We describe all such bijections f:G ightarrow Z_2^n, for a given quasigroup |G|=2^n, and describe such quasigroups for a given function f.