Theoretical and Applied Informatics

The problem of query selectivity estimation for database queries is critical for efficientquery execution by database management systems. A query execution method strongly depends on earlyestimated size of a query result. This estimation determines a data access method used later during thequery execution. The selectivity parameter is a fraction of table rows that satisfy a single-table querycondition. For a selection condition of a range query where an attribute has a continuous domain, theselectivity is equivalent to a definite integral form probability density function (PDF) of attribute valuesdistribution. For a compound selection condition based on many attributes we need a multidimensionalspace-efficient non-parametric estimator of multivariate PDF of attribute values distribution. A knownapproach based on Discrete Cosine Transform (DCT) spectrum as an representation of multidimensionalPDF is considered. The energy compaction property of DCT lets omit a region of spectrum coefficientswith small absolute values without significant losing an accuracy of selectivity estimation. An area ofrelevant spectrum coefficients is called a sampling zone. Results of experiments from previous worksshows that applying the reciprocal shape of the sampling zone gives the least selectivity estimation errorsubject to a predetermined size of the zone. The main result of this work is a theoretical confirmation of onlyexperimental results from previous works. The paper presents the proof of the theorem that the reciprocalshape of the sampling zone is asymptotically error-optimal. The proof is based on calculus of variationsand the isoperimetric problem.

The article introduces a novel Internet diagnosis utility - an open source IP packet snifferwhich captures TCP and UDP packets sent and received by a single Linux process only. Preliminary evaluation results are presented. The utility can be applied in the field of IP traffic classification.

Business Process Modelling Notation (BPMN) is a visual specification language without well-defined concepts for equivalences. This necessitates the establishment of fundamental notions that underpin the equivalences of BPMN processes. The main body of the paper is centered around the principle of substitutibility in which different types of equivalences of BPMN processes are formally described. Additionally, these results provide a basis for defining the behavioural equivalence of BPMN models. Our research investigation contributes to the field of business process management by developing a tight con-nection between BPMN and its associated equivalence notions.

In this article we analyse various methods of value approximation for Prolate Spheroidal Wave Functions (PSWF). As PSWFs are not given by explicit formula, for any application their values need to be calculated based on their properties and connection to other functions. We will focus on three approaches – Legendre polynomials, Eigenvalues of Matrix Operators and Hermite functions. We then create an implementation and test its effectiveness by using is as a base for band limited signal approximation algorithm.

This article describes security mechanisms used by 3rd-7th layers in OSI/ISO network model. Many of commonly used protocols by these layers were designed with assumption that there are nointruders. Such assumption was true many years ago. The network situation has been changed for last few years and we should realize that some properties of existing protocols may be abused. Moreover, we should exchange some of them or create new versions. There are some methods and guidelines concerning secure programming, but there is also lack of guidelines about creating secure protocols. Authors see the necessity of such guideline and this article is an attempt at analysing existing solutions and selecting some universal and important patterns.