Article aimed to the description of equivalent transformations that are allow to get at least one diagonal Latin square (DLS) from all main classes of DLS included in main class of given Latin square (LS) if they are exist. Detailed description of corresponding algorithms for LS of odd and even orders is given. Estimations for time and memory complexities are presented, algorithms are provided with detailed examples. Description of the results of diagonalization and canonization is shown. They allow to get collections of orthogonal diagonal Latin squares in a more efficient way comparing with direct usage of Euler-Paker method using volunteer distributed computing projects Gerasim@Home and RakeSearch on BOINC platform. The possibility of obtaining stronger upper and lower bounds for some numerical series in OEIS connected with DLS using suggested transformations is shown. Prospects for further application of these transformations using distributed software implementation of corresponding algorithms are outlined.

The main goal of the work was aimed to create a parallel application using a multithreaded execution model, which will allow the most complete and efficient use of all available computing resources. At the same time, the main attention was paid to the issues of maximizing the performance of the multithreaded computing part of the application and more efficient use of available hardware. During the development process, the effectiveness of various methods of software and algorithmic optimization was evaluated, taking into account the features of the functioning of a highly loaded multithreaded application, designed to run on systems with a large number of parallel computing threads. The problem of loading all available computing resources at the moment was solved, including the dynamic distribution of the involved CPU cores/threads and the computing accelerators, installed in the system.

In this paper, we describe the experience of setting up a computational infrastructure based on BOINC middleware and running a volunteer computing project on its basis. We characterize the first series of computational experiments and review the project’s development in its first six months. The gathered experience shows that BOINC-based Desktop Grids allow to efficiently aid drug discovery at its early stages.