Radioelectronics & Informatics

4-11

Authors: I. Grebennik, D. Grytsay, S. Shekhovtsov

In the article we deal with the optimal placement problem in manufacturing printing products. A special set of two-dimensional geometric objects bounded by circular arcs and line segments are introduced as mathematical models of real-life printing objects. We derive phi-functions, as well as normalized and pseudo-normalized phi-functions to describe the relations (non-overlapping, containment and distance constraints) between the geometric objects. A mathematical model of the optimal placement of printing objects is constructed and a solution strategy is proposed. Index Terms – cutting, phi-functions, printing objects, mathematical model, solution strategy.

17-22

Authors: VALERY SAPOZHNIKOV, VLADIMIR SAPOZHNIKOV, DMITRY EFANOV, VYACHESLAV DMITRIEV, MARIA CHEREPANOVA

Abstract – The article provides the method of formation of the sum code with minimum total number of undetectable errors. The code, suggested by authors, has the same number of check bits, as a classic Berger code, but also has a better detection ability, particularly within the area of low multiplicity errors in data vectors. New sum code allows to develop concurrent error detection (CED) systems of logic units of automation and computer devices with low equipment redundancy and a high percentage of error detection in controlled blocks.

26-29

Authors: OLEKSANDRA S. YEREMENKO, ALI SALEM ALI

This paper is devoted to the proposition of the algorithm of secure multipath routing with optimal balancing message fragments number in MANET. The work considered the concept of the threshold secret sharing scheme in relation to secure routing using non-overlapping paths for the message fragments transmission. Based on the analysis of disadvantages of existing mechanism SPREAD, it was proposed to improve the fragments allocation model, which had been reduced to the optimal balancing of message fragments number transmitted over the non-overlapping paths. Several optimality criteria were suggested as to the solution of balancing problem using Shamir`s scheme with or without redundancy. In the comparative analysis it was justified to use optimality criterion in practice, providing, on the one hand, minimization of dynamically managed upper bound number of fragments transmitted over separate non-overlapping paths in the network, and on the other hand –adaptation to security parameters (probability of compromise) of individual network elements: nodes, links and paths. Numerical examples of models with different optimality criteria of the solutions obtained, and their comparative analysis were presented. Within the proposed algorithm it is suggested to use the model under which the minimum number of fragments is transmitted by the worst path in terms of the probability of compromise, whereas their maximum number - by the best path. Keywords — Secure routing, MANET, probability of compromise, number of fragments balancing, non-overlapping paths.

37-41

Authors: PANKRATOV A., ROMANOVA T., KHLUD O.

The paper considers the problem of packing a given collection of ellipsoids of revolution into a rectangular container of minimal volume. Our ellipsoids can be continuos rotated and translated. A class of radical-free quasi-phi-functions is used for an analytical description of non-overlapping and containment constraints. We formulate the packing problem in the form of a nonlinear programming problem and propose a solution strategy, which allow us to search for local optimal packings. The actual search for a local minimum is performed by IPOPT. We provide computational results. Index Terms – packing, ellipsoids, continuous rotations, non-overlapping, containment, quasi-phi-functions, solution algorithm, nonlinear optimization