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pij0, i,jI, (Б) ji i, j i, j Sij = pij + pji. Sij = pij + pji. rij = ( pij - pji) / 2.

rij = pij /( pij + p ).

ji Степенная калибровка rij = pij /(1+ pij ).

rij = pij /(1+ pij ); rij = logT pij;

pijpji=1, pij>0, i,jI, (С) T>1.

rij = T pij /(1 + pij );

T > 0.

Турнирная калибровка rij = pij /( pij + pji).

rij = pij - pji;

_ pij+pji=Т, i,jI, (Т) rij = ( pij - pji)/ 2.

Вероятностная калибровка (В) rij = Tpij, rij = T( pij - pji );

_ pij+pji=1, 0pij1, i,jI, T > 0. T > 0.

Кососимметрическая rij = pij (sign pij + 1) / 2 + rij = ( pij + max pij ) / i, j калибровка + (max pij - pij ) / 2; /(2 max pij ) _ pij+pji=0, i,jI, (К) i, j i, j rij = T ( pij + max pij );

i, j T > 0.

Таблица1. Тождественные преобразования между способами представления отношений между объектами.

(ПС) отношения матрицы отношения матрицы кативные Количественные метризованные Качественные Аддитивные МультиплиПростая структура Простая отношения Качественные структура (ПС) матрицы кативные Количественные метризованные отношения Аддитивные матрицы Мультипли266 Mathematical Foundations of AI Соответствие между формами представления отношений между объектами Отношения, представленные в форме П1), являются заданными в качественной (квалиметрической) шкале. Последние три формы представления отношений между объектами, которые выражают количественную меру отношений, називают метризованными и говорят, что они отображают интенсивность отношений. Форма П2) називается еще аддитивным, а форма П4) - мультипликативным отношением. Между формами П2), П3), П4) существует взаимооднозначное соответствие ([Миркин, 1980], [Хованов, 1982]).

Для обработки результатов измерения количественных величин используется аппарат математической статистики. Для обработки статистическими методами результатов измерений в качественных шкалах, необходимо нечисловую информацию метризовать ([Литвак, 1982], [Бевз, 1989]), то есть погрузить в систему, производную от действительных чисел. Метризацией (оцифровкой ([Бевз, 1989], [Хованов, 1986]), арифметизацией ([Хованов, 1982])) квалиметрической шкалы называется построение соответствия между формой П1) и остальными формами. Не каждая реляционная система может быть изоморфно метризованной [Гильбурд, 1988]. С другой стороны, некоторые квалиметрические шкалы могут быть метризованы различными способами. Методы метризации квалиметрических отношений приводятся, например, в работах [Бевз, 1989], [Гнатиенко, 1993].

Библиография [Бевз, 1989] Бевз С.Н. Непротиворечивая метризация качественных признаков//Автоматика, 1989,№3,С.17-23.

[Гильбурд, 1988] Гильбурд М.М. Об эвристических методах построения медианы в задачах группового выбора // Автоматика и телемеханика. 1988. №7. С.131-136.

[Гнатиенко, 1993] Гнатиенко Г.Н., Микулич А.Ю. Методы метризации качественных ранжировок объектов //Киев.ун-т.Киев,1993.-10с.-Библиогр.: 6 назв. - Рус. - Деп. в УкрНИИНТИ 10.03.93, №432-Ук93.

[Дэвид, 1978] Дэвид Г. Метод парных сравнений. - М.: Статистика.1978.144 с.

[Загоруйко, 1999] Загоруйко Н. Г. Прикладные методы анализа данных и знаний. Новосибирск, издательство института математики, 1999.

[Кемени, 1972] Кемени Дж.Г., Снелл Дж.Л. Кибернетическое моделирование. М.: Советское радио. 1972. 192 с.

[Кендэлл, 1975] Кендэлл М.Дж. Ранговые корреляции. М.: Статистика.1975.214 с.

[Кини, 1981] Кини Р.Л., Райфа Х. Принятие решений при многих критериях: предпочтения и зимещения. М., 1981.

560 с.

[Ларичев, 1980] Ларичев О.И., Мошкович Ш.М. О возможностях получения от человека непротиворечивых оценок многомерных альтернатив/ Дескриптивный подход к изучению процессов принятия решений при многих критериях//Сб. трудов ВНИИСИ.1980.№9.С.58-66.

[Литвак, 1982] Литвак Б.Г. Экспертная информация: Методы получения и анализа. М.: Радио и связь. 1982. 184 с.

[Миркин, 1974] Миркин Б.Г. Проблема группового выбора. М.: Наука, 1974.-256с.

[Миркин, 1980] Миркин Б.Г. Анализ качественных признаков и структур. М.: Статистика. 1980. 319 с.

[Паниотто, 1982] Паниотто В.И., Максименко В.С. Количественные методы в социологических исследованиях.

К.: Наукова думка. 1982. 272 с.

[Паниотто, 1986] Паниотто В.И. Качество социологической информации. Методы оценки и процедуры обеспечения.К.:Наук.думка,1986.-207с.

[Хованов, 1982] Хованов Н.В. Математические основы теории шкал измерения качества/Изд-во ЛГУ. 1982.

[Хованов, 1986] Хованов Н.В. Стохастические модели теории квалиметрических хкал: Учебное пособие. Л.1986.80 с.

[Чеботарев, 1989] Чеботарев П.Ю. Обобщение метода строчных сумм для неполных парных сравнений//Автоматика и телемеханика. 1989. №8. С.125-137.

[Юшманов, 1990] Юшманов С.В. Метод нахождения весов, не требующий полной матрицы парных сравнений//Автоматика и телемеханика. 1990. №2. С.187-189.

[Larichev, 1989] Larichev O., Boichenko V., Moshkovich H., Sheptalova L. Modolling multiattribute information processing strategies a binary decision task/Org. Behav. and human perf. V.26. 1980.

Информация об авторе Григорий Н. Гнатиенко – Киевский университет им.Т.Шевченко, факультет кибернетики, докторант. Киев, Украина; е-mail: G.Gnatienko@veres.com.ua Intelligent Systems CLUSTER SUPERCOMPUTER ARCHITECTURE Andrey Golovinskiy, Sergey Ryabchun, Anatoliy Yakuba Abstract: The paper describes the architecture of supercomputer system of cluster type SCIT and the base architecture features used during this research project. This supercomputer system is put into research operation in Glushkov Institute of Cybernetics NAS of Ukraine from the early 2006 year. The paper may be useful for those scientists and engineers that are practically engaged in a cluster supercomputer systems design, integration and services.

Keywords: supercomputer, cluster, computer system management, computer architecture.

ACM Classification Keywords: C.1.4 Parallel Architectures. C.2.4 Distributed systems, D.4.7 Organization and Design 1. Introduction In 2004-2005 years small developer team from the Glushkov Institute of Cybernetics NAS of Ukraine built and put into research operation two high-performance supercomputer systems with cluster architecture SCIT-1 and SCIT2 on the basis of modern unicore Intel microprocessors. The developed supercomputers allow to solve essentially new challenges of the big dimension in the field of a science, economy, ecologies, an agriculture, in space branch and other branches.

Dynamics of managerial processes during task flow computing inside a supercomputer system, adaptation of existing and creation of new architectural means for maximization of global characteristics of supercomputer productivity is the investigation objects in the current work of research team.

2. Architecture Components of Cluster Supercomputer The architecture of the multiserver, cluster system is a multi-plane combination of hardware-software means, particularly at the level of interaction of the server operating systems, distributions of processes of computation on processors and synchronization of these processes, effective maintenance of queries to the centralized or distributed files systems.

Specific of tasks for the cluster computing. The supercomputer of cluster type is the computer system with asymmetrical multiprocessing and strongly connected nodes and task, intended for execution in a such computation environment, have features:

• each task consists of great number of interactive processes having an identical code, they are started on the different cluster nodes and each of them executes some part of common work;

• during the task execution processes can exchange intensively between themselves;

• interprocess data exchange results in smoothing of productivity of each process on speed of the slowest;

• each process, as a rule, occupies the large volume of main memory for the period of execution.

A cluster task is located in the user domestic catalogue and for implementation is got on competition basis two cluster resources - processor resource and timing resource. The long continuous execution of task is connected to an opportunity to not receive results in time (for example, from failures or at the large load by other tasks), therefore the double timing resources is given tasks – both full time of execution of task as the session time i.e.

268 Intelligent Systems time of noninterapted execution, after a session a check point keeping received intermediate result should be formed. The technology of programing with check points is one of basic components of organization of task execution, as allows repeatedly to interrupt execution and to proceed in it on intermediate results.

Simplified structure of supercomputer. The supercomputer of cluster type is the array of computing nodes, each of which is a multiprocessor server with symmetric mulitprocessing in the field of common main memory (SMP-architecture), incorporated by a few local areas networks of different purpose and productivity; from the array of computing nodes can be abstracted frontend servers (managing nodes) for the centralized process for handling of task executions. Besides this, there are the servers, specialized on the management by shareable files resources (file server) and external access of users to the cluster (access server) – see fig.1.

Fig. 1. Simplified cluster structure Some hardware and software features of SCIT supercomputers are resulted in table 1.

Table 1. SCIT clusters hardware characteristics SCIT-1 SCIT-Computing nodes quantity 24 Node processor quantity 48 (Xeon 2,67 GHz) 64 (Itanium2 1,4 GHz) Frontend quantity 1 Processor cache (Mbyte) 1 All main memory (GByte) 48 (DDR SDRAM PC-2100 ECC) 64 (DDR SDRAM PC-2100 ECC) Interconnect network Infiniband SCI (Scalable Coherent Interface) File managing network Gigabit Ethernet Gigabit Ethernet Storehouse (TByte) 1.6 (Common to both clusters) Operating system (Linux) Fedora Core 4 CentOS 4.Linux kernel 2.6.12 2.6.Global File system Lustre 1.4.5 Lustre 1.4.Parallel programming system Open MPI Open MPI, Scali Programmming language С, С++, Fortran-77 С, С++, Fortran-XII-th International Conference "Knowledge - Dialogue - Solution" The cluster operating system are chosen Linux FedoraCore4 and CENTOS 4.2, they are established both on frontend and computing nodes of clusters. As the root file system for computing nodes is used NFS, and as the distributed file system are chosen Lustre [1].

The cluster software accessible to the user includes for programming languages C/C++, Fortran compilers of the GNU and Intel different versions, for the parallel calculations - optimized libraries of ATLAS[2], BLACS[3], SCALAPACK[4], Intel MKL[5], application packages of GROMACS[6], WIEN2K[7], GAMESS[8] et al. As a parallel interface various realization of MPI interface - SCAMPI[9], OPENMPI[10] are used.

Task management and file exchange networks. In the environment of tasks management and file management two logical networks are allocated - management network (MN) and file exchange network (FEN).

FEN service generally should give opportunities:

• remote management of computing node through protocol of WakeOnLan;

• access of node to the data on a network configuration (protocols of DHCP);

• loadings of the operating system in a computing node (protocols of TFTP);

• access of node to root file system (protocols of NFS);

• deliveries at the computing node of the task data (protocols of NFS).

MN service generally case provides an opportunity of access to the node from outside for:

• operative management by a node;

• receptions of statistical information on loading of processors, employment of memory, the indication of gauges of temperature, speed of rotation of fans;

• start and further control of task processes.

Let’s consider in detail use of a network of data exchange for the process to start the cluster computing node.

Each node is configured on inclusion at reception by the network interface of the special package wake-on-lan and on the load through a network interface by PXE-protocol. A frontend sends the formed package through FEN and a node initiates the load process.

A node sends the broadcast inquiry and from the server DHCP which is established on a frontend, receives all data necessary for loading system, downloads a kernel and minimum root file system from the TFTP server, which is also established on the frontend, unpacks a kernel and starts its implementation.

Farther the process of initializing of the system, being based on received on DHCP data, mounts on NFS file system located at storehouse, does it by a root and completes initializing, having transferred management to the starting scripts located on the new root file system. Since this moment loading of system on a network or from a local disk does not differ practically. Further additional sections NFS with working data, by users directories and etc necessarily are mounted.

Such scheme supposed that root file systems at all cluster nodes are the same, essentially facilitates administration, update, installation of the new software, as works with all cluster entirely, and on orders reduces an opportunity to make a mistake. Root file systems of all nodes are identical, except for a few catalogues which really should be unique at everyone, but also they are located in main memory of node. Processes of each activated task, working as everyone on a separate node, all the same work in the same catalogue located at the storehouse, read and write from/to the same files.

As we see, practically all on the file input-output work is done on the data exchange network, therefore the requirements to throughput of this network very high. It is necessary to specify, that a «bottle neck» in this chart is the network interface of server, throughput of the network interface of node suffices much.

The start of task execution on the cluster nodes can be carried out by various ways depending on a task, i.e. a MPI-task is started by the command of mpirun, and the ordinary not parallel program can be activated by the command of ssh or rexec. For the operative control after the started task state, for its forced completion and liberation of resources busy at a task access is also used to the node on protocol of SSH, it non-obvious implies, that the node should be accessible.

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