Motivated by recent best case analyses for some sorting algorithms and based on the type of complexity we partition the algorithms into two classes: homogeneous and non-homogeneous algorithms.1 Although both classes contain algorithms with worst and best cases, homogeneous algorithms behave uniformly on all instances. This partition clarifies in a completely mathematical way the previously ment...

A concept of systolic dissemination of information in interconnection networks is presented, and the complexity of systolic gossip and broadcast in one-way (telegraph) and two-way (telephone) communication mode is investigated. The following main results are established: (i) a general relation between systolic broadcast and systolic gossip, (ii) optimal systolic gossip algorithms on paths in bo...

Approximation algorithms are used when we know a problem is hard. It is a way to consider optimization versions of function problems. For instance, given a 3-CNF formula, finding a maximal truth assignment is essentialy a MAX3SAT. Approximation algorithms return solutions that are close to the optimal in some way. So, if OPT (x) is the optimal solution for problem x, and A(x) is our approximate...

The paper deals with the cluster analysis and genetic algorithms and describes their basis. The application of genetic algorithms is focused on a cluster analysis as an optimization task. The case studies present the way of solution of two and three dimensional cluster analysis in MATLAB program with use of the Genetic Algorithm and Direct Search Toolbox. The way of its possible use in business...

Near-optimal gossiping algorithms are given for twoand higher dimensional tori. It is assumed that the amount of data each PU contributes is so large that start-up time may be neglected. For twodimensional tori, a previous algorithm achieved optimality in an intricate way, with a time-dependent routing pattern. In all steps of our algorithms, the PUs forward the received packets in the same way.

in this paper, we study the problem of minimizing the ratio of two quadratic functions subject to a quadratic constraint. first we introduce a parametric equivalent of the problem. then a bisection and a generalized newton-based method algorithms are presented to solve it. in order to solve the quadratically constrained quadratic minimization problem within both algorithms, a semidefinite optim...

The resourcefulness of people working in the area of cryptology is striking. A wonderfully diverse set of professionals capable of generating an almost endless stream of new, intriguing research problems and, fortunately—driven by the ever faster changing playing field of our information society and infrastructure under attack—capable of finding many ingenious and compelling solutions as well. ...

Prior to a three-way component analysis of a three-way data set, it is customary to preprocess the data by centering and/or rescaling them. Harshman and Lundy (1984) considered that three-way data actually consist of a three-way model part, which in fact pertains to ratio scale measurements, as well as additive "offset" terms that turn the ratio scale measurements into interval scale measuremen...