2017 № 1(34)





  4. Khairetdinov M.S., Poller B.V. , Britvin A.V., Sedukhina G.F.  ACOUSTIC-OPTICAL SYSTEM OF ULTRALOW FREQUENCIES 




Zhusupbaev A., Toktoshov G.Y.

Institute of theoretical and applied mathematics, 720071, Bishkek, Kyrgyz Republic
Institute of Computational Mathematics and Mathematical Geophysics SB RAS, 630090, Novosibirsk, Russia


UDC 519.8:624.9

The paper deals with one of the applied problems in the design and  modernization of the distribution points of the various services (eg, gas,  oil, and water) --- the problem of the optimal distribution of production and  distribution of resources between consumers and suppliers, taking into  account a variety of restrictive conditions. In this regard, the topic under  consideration, relating to the design and development of the mathematical  apparatus to describe, analyze, and optimize network engineering maintenance  vehicle type is relevant.

In this paper, engineering support network is seen as a hierarchical system of the vehicle type, two-stage, respectively solved the problem of  accommodation with a nonlinear objective function. It is assumed that  resources (oil, gas, water, etc.) are transferred in this system from producers to consumers through processing by points connections (transport  channels). Such systems are characterized by the presence of so-called fixed  costs to be made regardless of the target volume  roduction and processing  (gas, oil, etc.). The account in the models of these and similar factors  leads to the appearance of their objective functions that do not possess the  property of continuity. Therefore, the problem of resource allocation in 
hierarchical networks, is seen as a two-stage problem of placing items resource production and distribution with discontinuous objective function. This class of problems, which bears the character of multi considerably complicates the search for an extremum of the objective function, and can not be solved in the general case. Thus, there is a need to develop a new method of solving the problem, when the functions that determine the cost of production, transportation and processing of products are non-linear.

In this regard, the aim of this work is to develop new mathematical models and methods for analysis and optimization of engineering support transport-type networks with a hierarchical structure. The goal is achieved  as a result of research and development of the mathematical apparatus and optimization techniques for the design and optimization of engineering support such as transport networks, taking into account the various restrictive conditions of feasibility, natural, nvironmental, situational and character, as well as legal and budgetary constraints of the region.

Note that the distribution of production and resource allocation problems have a wide range of applications that arise when designing of engineering networks for different purposes, in problems of logistics facilities and power systems, planning and reconstruction transport-type networks, routing service networks and other areas. 

The paper studied and proved a sufficient condition for the applicability of the method of successive two-step calculation for the problem of locating  the production and processing of non-linear functions of transport,  operating costs and xpenses for processing at various restrictive conditions. A combinatorial method for optimizing the placement based on the method of consecutive calculations, which allows to calculate the best option to deploy elements of communications and network engineering plan (volume) of the transported goods from sources to consumers by the criterion of minimum total cost of production of the raw material, its processing and transportation. The proposed method makes it possible, though, and by the partial sorting, finding the global extremum multiextremal problem with any degree of accuracy.

The proposed methods and models allow to carry out a reliable analysis and optimization of engineering support networks and can be used in the design organizations involved in the design, construction and operation of networks for different purposes. 

Key words: networks location problem, the method of successive calculations, placement plan, the optimal output of production.

1. Lotarev D. T. Neformalnye opisatelnye modeli transpotnykh kommunikatsiy, transpotnykh setey I territoriy v zadachakh o prokladke putey I kommunikatsiy [Unformal descriptive models of transport communications, transport networks and territory in the problem of construction of ways and communications] // Trudy ISA RAN. 2009. V. 46. P. 259–273.
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9. Kosyakov S. V. Myagkie vychisleniya v postrornii kart zonirovaniya territorij po parametram system energosnabzheniya [Soft computing in mapping zoning by the parameters of power supply systems] // S. V. Kosyakov, S. S. Novoseltseva, A. M. Sadykov // International scientific-technical conference The state and prospects of development of electrotechnology. Ivanovo, 2013. P. 338–341.
10. Prilutskiy M. X., Afraiymovich L. G. Raspredelenie resursov v ierarkhicheskikh sistemakh transportnogo tipa: uchebnoe posobie [Distribution of resources in hierarchical systems of transport type: textbook] / M. X. Prilutskiy, L. G. Afraiymovich. Nizhny Novgorod. 2007.
11. Erzin A. I. Zadachi marshrutizatsii: uchebnoe posobie [The routing problem: textbook] / A. I. Erzin, JU. A. Kochetov. Novosibirsk, 2014. 
12. Lange E. G., Zhusupbaev A. Kombinatorniy metod resheniya zadachi razmesheniya [Combinatorial method for solving location problem]. Frunze, 1991.
13. Cherenin V. P. Reshenie nekotorykh kombinatornikh zadach optimalnogo planirovaniya metodom posledovatrlnikh raschetov [The solution of some combinatorial problems optimal planning by methods of successive calculations]. Moscow, 1962. 
14. Zhusupbaev A., Sharshembieva F. K. Reshenie dvukhetapnoy zadachi razmesheniya s nelineynoy tselevoy funktsiey [The solution of the two-stage location problem with nonlinear objective function] // Vestnik KNU. 2013. Vypusk 1. P. 21–29.
15. Asankulova M., Zhusupbaev A. Optimizatsiya dobichy I raspredeleniya sirya mezhdu potrebitelyami v zavisimosti ot perioda[Resources extraction and distribution optimization between consumers depending on the period] / Modern problems of science and education. 2016. N 4. P. 7–12.

Bibliographic reference:  Zhusupbaev A., Toktoshov G.Y.  One problem of the optimization resource distribution in hierarchical networks //journal “Problems of informatics”. 2017, № 1. P. 2-14.


Rodionov A. S.

Institute of Computational Mathematics and Mathematical Geophysics of SB RAS, 630090, Novosibirsk, Russian Federation


UDC 519.17

Tasks of obtaining and usage of exact cumulative expected values of some indices of a network's structural reliability, such as k-terminal probabilistic connectivity (k-TPC), average pairwise connectivity (APC) and expected size of a subnetwork that contains some special node (MENC) are considered in the paper.  While first index is well known and explored, last ones are not so. Note that APC characterizes network from a point of view of uses (it corresponds to a probability of  stablishing an arbitrary connection), and MENC is very important for stimating quality of a sensor or other monitoring network. Random non-oriented random graph with reliable nodes and unreliable edges that fails independently is used as a model of a network. At the same time the proposed approach can be used in the case of unreliable nodes also. The factoring method, exhaustive search, methods of reduction and decomposition are used as a base. Expected values are used for unambiguous decision making about network's reliability, designing evolutionary algorithms for structural optimization and obtaining approximate expected values that are more precious than cumulative ones obtained to the moment.

Exact cumulative expected values (lower - LB, and upper - UB) change (at least one of them) after obtaining value of an index used for some new realization of a network's structure in such a way, that after obtaining value of this index for a last possible realization both LB and UB become equal to an exact value of an index under consideration. The main idea is rather obvious one: when some values of an index with probabilities of corresponding realizations are obtained, we assume that all other realizations have possible minimal (for LB) or maximal (for UB) value of an index. This guarantees that exact value lays between LB and UB and that after last step LB, UB and exact value of and index are equal.

Key words: network reliability, reliability indecies, estimation, optimization.

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Bibliographic reference: Rodionov A.S. Cumulative estimated values of structuralnetwork'sreliability indices and their usage //journal “Problems of informatics”. 2017, № 1. P. 15-24.


Biyashev R.G., Kalimoldayev M.N., Rog  O.A.

Institute of Information and Computational Technologies, 050010, Almaty, Republic of Kazakhstan


UDC 004.94

In this paper we put a definition, formulated principles and built a formal  model for the typed attribute-based access control and its version, namely multi-criteria typed attribute-based access control.  Hierarchical semantic modeling system has been developed allowing designing  different models of access control. It consists of a metamodel, specific models obtained from it, and access matrices corresponding to that models. The proposed typed attribute-based access control method is based upon the concept of actively developed now attribute-based access control (ABAC). The essence of ABAC lies in the fact that the entities are assigned attributes which form access control criteria. Developing solutions for the subject to access an object is based on the calculation of attribute values. The positive quality of ABAC is its universality and flexibility. Hence, the ABAC can serve as a means to create different access control policies performing tasks of protection of information, which are characteristic to a specific organization. In particular it can represent such the most widely spread models as DAC, MAC, RBAC. On the other hand, the complexity of the implementation and lack of formal models pointed out by many researchers hamper the wide use of ABAC.

We propose a formal model for typed attribute-based access control model and a corresponding model for multi-criteria typed attribute-based access control. The idea of this model is based upon a notion of a type of the access control attributes. The type defined on several levels as a mathematical object, constitutes a semantic modeling system, which is intended to assign the semantic values to the names of the model. First, it assigns values to the names of the metamodel, thus forming a certain access control model, such as DAC, MAC or RBAC. Then during the stage of the functioning of the access control system based upon the model obtained, the semantic modeling system assigns values to the attributes of the entities  which belong to the access control matrix. Performing operations on the attribute values of the same type as well as on their structured subsets reduce the computational complexity, speeds up the calculation and  facilitates the administration process. Systems containing several independent types are able to perform multi-criteria access control.

Key words: access control task subject area, semantics, typed attribute-based access control, attribute type, semantic modeling system, metamodel, access control model, access matrix.

1. Devyanin P. N. Modeli bezopasnosti komp’yuternyh sistem. Upravlenie dostupom i informacionnymi potokami. Uchebnoe posobie dlya vuzov. M.: Goryachaya liniya-Telekom, 2011. 
2. Hu V.-C., Ferraiolo D., Kuhn R., Schnitzer A., Sandlin K., Miller R., Scarfone K. NIST Special Publication 800–162. Guide to Attribute Based Access Control (ABAC). Definition and Considerations // NIST National Institute of Standards and Technology. [Electron. res.]. http://dx.doi.org/10.6028/NIST.SP.800-162. Jan. 2014.
3. Jin X., Krishnan R., Sandhu R. A unified attribute-based access control model covering DAC, MAC and RBAC // Proceedings of the 26th Annual IFIP WG 11.3 conference on Data and Applications Security and Privacy (DBSec’12). 2012. P. 41–45. 
4. Bijon Kh., Krishnan R., Sandhu R. Constraints Specification in Attribute Based Access Control // IEEE/ASE Science Journal. 2013. V. 2. N 3. P. 131–144.
5. Biyashev R. G., Kalimoldaev M. N., Rog O. A. Polimorfnaya tipizaciya sushchnostej i zadacha konstruirovaniya mekhanizma mnogokriterial’nogo razgranicheniya dostupa // Izvestiya NAN RK. Seriya fiziko-matematicheskaya. 2014. N 5. P. 33–41.
6. Biyashev R. G., Kalimoldaev M. N., Rog O. A. Konstruirovanie sistem mnogokriterial’nogo atributnogo razgranicheniya dostupa v oblachnyh strukturah // Odinnadcataya Mezhdunarodnaya Aziatskaya SHkola-seminar Problemy optimizacii slozhnyh sistem Kyrgyzskaya Respublika, Issyk-Kul’skaya oblast’, g. CHolpon-Ata, 27 iyulya — 7 avgusta 2015 g. P. 148–152.
7. Biyashev R. G., Kalimoldaev M. N., Rog O. A. Logicheskij podhod k organizacii mnogokriterial’nogo atributnogo razgranicheniya dostupa // Sovmestnyj vypusk po materialam mezhdunarodnoj nauchnoj konferencii Vychislitel’nye i informacionnye tekhnologii v nauke, tekhnike i obrazovanii (CITech-2015) (24–27 sentyabrya 2015 g.) Vychislitel’nye tekhnologii. T. 20, Vestnik KazNU im.Al’-Farabi, seriya Matematika, mekhanika i informatika. N 3 (86) CH. 1. P. 275–278.
8. Biyashev R.G., Kalimoldaev M.N., Rog O.A. Mnogokriterial’noe atributnoe razgranichenie dostupa v sovremennyh vychislitel’nyh sredah // Trudy Mezhdunarodnoj nauchno-prakticheskoj konferencii Informacionnye i telekommunikacionnye tekhnologii: obrazovanie, nauka, praktika, Almaty, Kazahstan, 3–4 dekabrya 2015 g., T. 2. P. 67–70.
9. Biyashev R. G., Kalimoldaev M. N., Rog O. A. Predstavlenie ogranichenij modelej atributnogo razgranicheniya dostupa // Izvestiya NAN RK. Seriya fiziko-matematicheskaya. 2016. N 1. P. 58–65.

Bibliographic reference: Biyashev R.G., Kalimoldayev M.N., Rog O.A. Typed attribute-based access control semantics modeling //journal “Problems of informatics”. 2017, № 1. P. 25-37.


Khairetdinov M.S.*, Poller B.V.**, Britvin A.V.**,  Sedukhina G. F.*

Novosibirsk State Technical University, 630073, Novosibirsk, Russia
*Institute of Computational Mathematics and Mathematical Geophysics SB RAS, 630090, Novosibirsk, Russia
**Institute of Laser Physics SB RAS, 630090, Novosibirsk, Russia


UDC 534:621.382

Studying of questions acoustic-optical interactions have old history and they are connected, basically, with researches of diffraction of light in ultrasonic and radio-frequency ranges. Questions acoustic-optical interactions in area on ultralow practically not investigated. It is in many respects caused by absence of special acoustic radiators in this range of frequencies for carrying out of regular researches. In too time today there are seismic vibrators which are capable along with seismic oscillations in the earth to radiate on ultralow frequencies acoustic oscillations in atmosphere. Centrifugal vibrators CV-100 and CV-40, in particular, concern them. Acoustic oscillations from them are registered on removals to hundred kilometers and more. It opens possibilities of carrying out of regular experimental researches on acoustic-optical interactions in area ultralow frequencies. Authors of the present work offer an original method for study of acoustic-optical interactions on ultralow frequencies with powerful seismic vibrators as sources of acoustic oscillations. Along with the general-theoretical importance of such researches there is a great demand for them in connection with the decision of some the important applied problems, in particular, an acoustic location, the security alarm system, etc.

The description developed by author's acoustic-optical systems as a part of vibrator CV-40, the optical stand with a laser radiator capacity to 6 Вт in the length of wave 850--930 nanometers, frequency of repetition of impulses 1 kHz, the complete set of measuring acoustic stations and a meteorological station is resulted. Results of the executed modeling and natural experiments in which acoustic and optical oscillations were simultaneously registered are presented. Registration of acoustic oscillations is carried out along a line of distribution of a measuring laser beam on base 302 m, removed from a source of acoustic oscillations- of vibrator CV-40 on 920 m. By means of the ultra resolving spectral analysis processing of the received data is carried out. 

The noise immunity of reception of discrete frequency signals from vibrator CV-40 in a range of 8.5--10.5 Hz and also density of noise distribution are  estimated. The smaller noise immunity of optical reception in comparison with direct acoustic reception is revealed in 2.5 times. The density of distribution of noise in the optical channel is approximately described by the normal law. 

The further development of works is connected with application of a two-beam laser measuring line and use of phase methods of detection for increase of sensitivity of reception of acoustic fluctuations by means of a laser measuring line.

Key words: seismic vibrators, optical stand, natural experiments, results of data processing.

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3. Alekseev A. S., Glinsky B. M., Kovalevsky V. V., Khairetdinov M. S. et al. Active seismology with powerful vibration sources. Branch Geo of SB RAS Publ. House, Novosibirsk, 2004.

Bibliographic reference:  Khairetdinov M.S., Poller B.V., Britvin A.V., Sedukhina G.F.  Acoustic-optical system of ultralow frequencies //journal “Problems of informatics”. 2017, № 1. P. 38-51.


Kholmonov  S.M.

Samarkand State University, 140104, Samarkand, Uzbekistan


UDC 658.512.011

In traditional monitoring systems of industrial-technological complexes with non-stationary objects of control the quality of casual time series (CTS) identification and data accuracy increase up to the required level is ensured by involving difficult analytical relationships defined in the form of differential, difference, recurrence equations, which are realized by high iterative algorithms. Optimization of identification and data processing is ensured by adjustment parameters of CTS identification model using difficult recurrence relationships when conditions provide availability of extensive prior knowledge.

The perspective approach to elimination of high-iterative method of calculation under a priori insufficient of data and uncertainty during developing mechanisms of regulatory and adjustment of non-stationary objects parameters is to develop methods and models that combine opportunity, properties and features of neural networks (NN) with mechanisms for extraction and use of useful knowledge, hidden properties, specific characteristics of CTS. In this case the mathematical apparatus of soft computing successfully completes composition of known methods and algorithms, constructed on the basis of statistical and dynamic approaches, and also expands the capacity of existing toolkits. The important task of NN
using is training of the network, and known algorithms of forward and back-propagation of errors are based on methods of least squares, gradient optimization and their modifications that lead to labor intensive computing of precise values of the optimization functional, especially when it is necessary to solve tasks with high dimensionality.

In this work the mathematical model of data processing optimization is formalized in view of application the mechanism of adjustment, where the task of optimization of data processing is to regulate the value of output result of identification $u(\cdot)$ on the basis of selecting the suboptimal set of NN training parameters. 

Concept of probability, evolutionary computation, adaptation of parameters of computational schemes of NN structural components are used for improvement and development methods to optimization data processing and solution of tasks of search during NN training. Solution of designing of adapted modified computational schemes of NN structural components is to form a sub-optimal set of parameters such as weights of neurons, synaptic connections coefficients, type of activation function, rational architecture, functional relationships inputs and outputs

Use of NN radial-basis activation functions gives to network the feature of self-tuning and self-adaptation, and allows to carry out dynamic adjustment of parameters of computational schemes of NN structural components. The mechanism for use the methods of parameters adjustment on the basis of selection fractal characteristics, segmentation, filtering and analysis is proposed to empower and improve the adequacy of models to describe objects with non-stationary components of CTS.

The developed program complex includes module of identification and synthesis of dynamic models described non-stationary objects, modules of  modified NN training on the basis of radial-basis functions, segmentation, CTS filtering, adjustments of parameters, results of which testing are received at 538 training sets generated from set of CTS measurements.

The study showed that during implementation of developed methods and algorithms for the identification, the number of areas accounted for the change of quasi-stationary segments increased on 10--12%, and the number of  accounted classes of non-stationary events increases on 20--30% due to determination and formation of sub-optimal sets, application of segmentation mechanisms, nonlinear filtering and NN training, and this undoubtedly proves obvious of optimization of data processing based on synthesis of statistical, dynamical and neuro networking models.

Key words: non-stationary object, data processing, identification, optimization, training of neural network, adjustment of parameters, segmentation, nonlinear filtration.

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Bibliographic reference:  Kholmonov S.M. Optimization of data processing on the basis of modified training of neutral network and segmentation of casual time processes //journal “Problems of informatics”. 2017, № 1. P. 52-61.


Moiseenko V.V., Rodionov  A.S.

Institute of Computational Mathematics and Mathematical Geophysics of Siberian Branch of Russian Academy of Sciences, 630090, Novosibirsk, Russia


UDC 510-519.24

The paper is devoted to examination of co-authorship of researchers from different age groups in papers prepared in an institute of natural sciences. Research bases on example of real statistics of a special institute using databases that include personnel and productive indices. We show that number and structure of coauthors depends on a scientist's age. The dynamics of  number of coauthors per paper during 2001--2015years is shown also. 

We consider the following indices:

1) part of researchers who have publications made in co-authorship;
2) average number of co-authors per researcher in each age group;
3) average number of co-authors per paper for a researcher in each age group;
4) average number of co-authors per one researcher in given age group in the case of co-authorship with researchers from other age groups;
5) average number of co-authors per paper for a researcher in given age group in the case of co-authorship with researchers from other age groups.

The following main conclusions are done based on our data:

1) Most active in co-authorship are researcher in the 1\textsuperscript{st} age group (up to 35 years old). This may be explained by the fact that young researchers usually help their supervisors and so good part of ideas and problem statements in the papers belongs to co-authors from older groups. Next peak of co-authorship corresponds just to oldest (5th) group. Researcher in this group rarely are active in personal researches, they mostly lead researches performed by doctoral students and young scientists.
2) We may state that average number of co-authors in papers devoted to applied mathematics is not as large as in social or natural (chemistry, biology, medicine, etc.) sciences, but it is larger when a paper needs numerical experiments, that is programming and executing proposed algorithms, which means including programmers into a team.
3) There is clear trend to increasing number of papers and co-authors in last years. This may be explained by the following consideration: number of  publications became main index of a researcher's quality. In this case it is quite natural that instead of publishing one paper per year without co-authorship or with 1-2 co-authors, researchers agree that it is easier and better for annual reporting publish 3--5 papers per year with 2-4 or even more co-authors.

Key words: scientific process, subsystem, age group, co-authorship, average number of co-authors, publishing scientific paper.

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Bibliographic reference:  Moiseenko V.V., Rodionov A.S. Age dependency of co-authorship in scientific researches in academia //journal “Problems of informatics”. 2017, № 1. P. 62-73.


Malyshkin* V.E., Perepelkin* V.A., Schukin** G.A.

Institute of Computational Mathematics and Mathematical Geophysics SB RAS, 630090, Novosibirsk, Russia
*Novosibirsk State University, 630090, Novosibirsk, Russia
**Novosibirsk State Technical University, 630073, Novosibirsk, Russia 


UDC 004.021

The paper presents a scalable distributed algorithm for static and dynamic data allocation in LuNA fragmented programming system. The proposed algorithm takes into account data structure of the application numerical model executed, enables static and dynamic load balancing and can be used with various network topologies. Implementation of numerical models on multicomputers with large number of computing nodes is a challenging problem in the domain of high-performance parallel computing. Effective resources allocation and balancing strategies are necessary to achieve good efficiency and scalability of parallel programs. LuNA is a fragmented programming system which is being developed in Supercomputer Software Department of Institute of Computational Mathematics and Mathematical Geophysics SB RAS. LuNA’s main objective is automation of construction of parallel programs, which implement large-scale numerical models for large-scale multicomputers.

In LuNA system an application algorithm is represented as two sets: a set of immutable data pieces (data fragments, DF) and a set of side-effect free computational processes (computational fragments, CF). All these fragments can be distributed over computational nodes of a multicomputer. Each DF is produced by one CF and can be used as an input by other CFs; each CF is executed only once and requires values of all its input DFs to be gathered on a single node for its execution. Execution of a program is managed by LuNA's runtime system. The runtime system performs distribution and migration of DFs and CFs over nodes of a multicomputer and deliverance of input DFs to their corresponding CFs to provide execution of all CFs in the program.

There are several steps in processing of DFs and CFs. Each DF must initially be assigned to a node for its storage and be allocated on this node. Each CF must be assigned a node for its execution and also be allocated on the node. Efficiency of LuNA program execution (in terms of running time, memory consumption, communications amount, etc.) heavily depends on CFs and DFs distribution. To achieve suitable efficiency, during execution of a program
fragments may be transferred between nodes in order to equalize workload. Such dynamic load balancing is also performed by the runtime system. The algorithm described in the paper is used as for initial data allocation, as well as for
dynamic load balancing. Although its description is given in respect to data fragments only, in the same way it can also be used (and is used actually) for managing allocation of computational fragments.

First, a mapping of data fragments to a range of integer indices must be constructed. The mapping is an input for the algorithm described. The mapping is expected to map dependent neighboring data fragments on the same or close indices. Construction of such a mapping is a complex task, which is out of the scope of the paper. Construction of a suitable mapping, a knowledge of algorithm structure is required, human help is expected. To create a mapping of a multi-dimensional data structures to the one-dimensional index range space-filling curves (such as Hilbert space-filling curve) may be used to preserve data neighborhood. The mapping is a constant function during execution of a program, thus it can
be computed on any node without communications.

Second, the given indices range is split into segments with number of segments equal to the number of computational nodes. Each node is given its own segment, neighboring nodes in a line topology receiving neighboring segments. Each data fragment will be allocated on the node containing index of its mapping. For that, assuming the data fragment was produced on some node, first its mapping is computed and then, if necessary, the fragment is
transferred across neighboring nodes until its final node is found. Because indices are ordered and for each node its neighbors are known, direction of fragments' movement in the line of nodes can always be determined at any node. In such way data allocation requires only local communications between neighboring nodes.

For the sake of dynamic load balancing the mapping of segments of indices to nodes can be changed. First, for each index in a segment its workload is evaluated. Formulas for workload evaluation can be different, for example value of workload can be proportional to a volume of memory occupied by data on the node. Node's workload is computed as sum of its indices workloads. Second, workloads of neighboring nodes are compared periodically. If the workload difference exceeds a threshold, load re-balancing will be performed. For that neighboring nodes shift common border of their segments (from overloaded node to underloaded one), causing DFs mapped to migrate thus equalizing workload. Because order of indices is preserved during border shift, data locality is preserved too. Load balancing algorithm is distributed (executes on each node) and uses only local communications.

Usage of only local communications for data allocation and load balancing makes proposed algorithm scalable to a large number of computational nodes, because no global synchronization (that can impede scalability) is used.

Testing of the algorithm has shown its potential for scalability; performance of fragmented program for problem used was just several times worse than of usual MPI implementation for the same problem, given that MPI implementation with dynamic load balancing takes more time and effort to program instead of LuNA implementation, where data allocation and load balancing are implemented automatically.

Key words: scalable distributed system algorithm, dynamic data  allocation, distributed algorithms with local interactions, fragmented programming technology, fragmented programming system LuNA.

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Bibliographic reference:  Malyshkin V.E., Perepelkin V.A., Schukin G.A. Distributed algorithm for data allocation in luna fragmented programming system //journal “Problems of informatics”. 2017, № 1. P. 74-88.