Search

We research a scheduling algorithm for a feasible schedule construction on one machine by the total earliness of jobs minimization criterion. We propose an improvement to this algorithm. During the research, we have developed a software system to verify reliability of the algorithms. We compared the schedules built by the algorithm with those constructed by an exhaustive enumeration. We calculated the percentage of a non-exact schedule construction by the investigated algorithm for different characteristics of the schedule. The object of research is the process of schedules' optimization and their investigation. The purpose of the paper is to increase the efficiency of feasible schedules construction process for one machine in the presence of penalties for jobs completion prior to their due dates. We need to use appropriate economic and mathematical methods, in particular those from scheduling theory, to organize the production and planning on an enterprise efficiently. Scheduling problems have a great application value today. Rapid development of communication and electronics technologies increasingly requires the construction of schedules. The schedules are related to functioning of industrial enterprises and the service sector, education, transport and many other areas. Tasks of scheduling theory include study of the computational complexity of the problems and development of exact, approximation and heuristic algorithms for their solution. Most papers are devoted to combinatorial approaches' development. However, as practice shows, possibilities of combinatorial algorithms are substantially limited by the dimension of the problems they solve. This is why we believe in importance of the research and improvement of the scheduling algorithm to minimize the total earliness of jobs on one machine. We use combinatorial optimization methods, scheduling theory, heuristic algorithms and statistical analysis. The scientific novelty of the results consists in modification to the existing scheduling algorithm that minimizes the total earliness on one machine. New algorithm has better efficiency than the existing ones. [ABSTRACT FROM AUTHOR]

The analysis of information flow protection systems, using asymmetric cryptalgorithms, on the basis of which the shortcomings of existing approaches of realization of the operations of modular exponentiation at encrypting/decrypting, namely - use of keys, encryption units and crypto-conversion module up to 2048 and 4096 bt, which reduces the time characteristics, was made in this work (thesis). It was established, that one of the perspective approaches concerning the solution of this class of tasks is use of the system of residue classes (SRC), which has several advantages in comparison with the binary one - conducting operations in parallel and digit capacity decrease of the operands, which do not exceed digit capacity of the selected SRC modules set. These drawbacks concern transfer from SRC to the decimal number system, namely the need to search for the reverse element by module, that is, the basis numbers. The thesis states that there are modules sets, which form the perfect SRC form (basic numbers are equal to 1) and modified perfect SRC (basic numbers are equal to ±1), which significantly reduces the time complexity of the transfer. Theoretical foundations of improvement of implementation of asymmetric El-Gamal cryptoalgorithm on the basis of joint use of SRC and vector-modular algorithm of modular multiplication, which made it possible to parallelize the process, to reduce time complexity and to improve performance of encrypting/decrypting process were given. [ABSTRACT FROM AUTHOR]

We suggested a method of digital signing based on mathematical apparatus of recurrent Vk sequences. The analysis shows that, overall, the method has approximately the same level of cryptographic reliability and computational complexity as the known analogues. However, under certain circumstances, the method provides for a significant speed increase of signature checking procedures, as well as increase of reliability of the whole digital signature process. [ABSTRACT FROM AUTHOR]

Reverse engineering of gene regulatory networks is an intensively studied topic in Systems Biology as it reconstructs regulatory interactions between all genes in the genome in the most complete form. The extreme computational complexity of this problem and lack of thorough reviews on reconstruction methods of gene regulatory network is a significant obstacle to further development of this area. In this article the two most common methods for modeling gene regulatory networks are surveyed: Boolean and Bayesian networks. The mathematical description of each method is given, as well as several algorithmic approaches to modeling gene networks using these methods; the complexity of algorithms and the problems that arise during its implementation are also noted. [ABSTRACT FROM AUTHOR]