Optimal Paralleling for Solving Combinatorial Modelling Problems using Graphics Processing Units
The paper considers possibility of combinatorial GMDH algorithm computational speedup by means of programs paralleling for computing on graphics processing units. The scheme of algorithm with successive complication of structures providing the uniform loading on all multiprocessors of graphic card i...
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| Date: | 2012 |
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Міжнародний науково-навчальний центр інформаційних технологій і систем НАН та МОН України
2012
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| Cite this: | Optimal Paralleling for Solving Combinatorial Modelling Problems using Graphics Processing Units / S. Yefimenko // Індуктивне моделювання складних систем: Зб. наук. пр. — К.: МННЦ ІТС НАН та МОН України, 2012. — Вип. 4. — С. 43-47. — Бібліогр.: 4 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1859586922279600128 |
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| author | Yefimenko, S. |
| author_facet | Yefimenko, S. |
| citation_txt | Optimal Paralleling for Solving Combinatorial Modelling Problems using Graphics Processing Units / S. Yefimenko // Індуктивне моделювання складних систем: Зб. наук. пр. — К.: МННЦ ІТС НАН та МОН України, 2012. — Вип. 4. — С. 43-47. — Бібліогр.: 4 назв. — англ. |
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| description | The paper considers possibility of combinatorial GMDH algorithm computational speedup by means of programs paralleling for computing on graphics processing units. The scheme of algorithm with successive complication of structures providing the uniform loading on all multiprocessors of graphic card is proposed.
У роботі розглядається можливість підвищення ефективності комбінаторного алгоритму МГУА за допомогою розпаралелювання обчислень на графічному процесорі. Запропоновано схему алгоритму з послідовним ускладненням структур, яка забезпечує рівномірне навантаження на всі мультипроцесори графічної карти.
В работе рассматривается возможность повышения эффективности комбинаторного алгоритма МГУА с помощью распараллеливания вычислений на графическом процессоре. Предложена схема алгоритма с последовательным усложнением структур, обеспечивающая равномерную нагрузку на все мультипроцессоры графической карты.
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| first_indexed | 2025-11-27T11:05:42Z |
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Yefimenko S.M.
Індуктивне моделювання складних систем, випуск 4, 2012 43
УДК 519.254
OPTIMAL PARALLELING FOR SOLVING COMBINATORIAL
MODELLING PROBLEMS USING GRAPHICS PROCESSING UNITS
S.M. Yefimenko
International Research and Training Centre of Information Technologies and Systems
of the NAS and MES of Ukraine
syefim@ukr.net
У роботі розглядається можливість підвищення ефективності комбінаторного алгоритму
МГУА за допомогою розпаралелювання обчислень на графічному процесорі. Запропоновано
схему алгоритму з послідовним ускладненням структур, яка забезпечує рівномірне
навантаження на всі мультипроцесори графічної карти.
Ключові слова: індуктивне моделювання, комбінаторний алгоритм МГУА, паралельні
обчислення, графічний процесор
The paper considers possibility of combinatorial GMDH algorithm computational speedup by
means of programs paralleling for computing on graphics processing units. The scheme of
algorithm with successive complication of structures providing the uniform loading on all
multiprocessors of graphic card is proposed.
Keywords: inductive modelling, combinatorial GMDH algorithm, parallel computing, GPU
В работе рассматривается возможность повышения эффективности комбинаторного
алгоритма МГУА с помощью распараллеливания вычислений на графическом процессоре.
Предложена схема алгоритма с последовательным усложнением структур, обеспечивающая
равномерную нагрузку на все мультипроцессоры графической карты.
Ключевые слова: индуктивное моделирование, комбинаторный алгоритм МГУА,
параллельные вычисления, графический процессор
1 Introduction
A problem of modeling by experimental data consists in dependence construc-
tion between input and output variables of an object or process being modeling. In
case of combinatorial algorithms use the stage of parameters estimation requires
high-powered computational resources, because of exponential dependence of com-
putational complexity on arguments amount. That is why available computer
resources have to be applied completely. In this case it is advisable to use:
− the high-speed methods of parameters estimation based on the recurrent algo-
rithms for solving of linear equations systems [1];
− paralleling of computing using multiprocessing cluster systems [2].
In the paper we will consider the possibility of using GPU-based parallel com-
puting for solving combinatorial modelling problems.
Optimal Paralleling for Solving Combinatorial Modelling Problems
Індуктивне моделювання складних систем, випуск 4, 2012 44
2 GPU-based parallel computing
Computations on graphics processing units (GPU) are enjoying wide popular-
ity lately. It is related to that computational capabilities of GPU have been racing up.
State-of-the-art graphics processors possess the enormous productivity that substan-
tially exceeds productivity of central processing units (CPU). Their availability to be
used for solving computational problems is being more and more catching in this
connection. For an example comparisons between computer systems performance us-
ing Intel processors and video cards of ATI [3] are showed on figures 1 and 2.
The reason for better performance of systems on the bases of GPU is that GPU
is specialized for compute-intensive, highly parallel computation. Combinatorial al-
gorithms are known to be well-parallelized and therefore can be effectively executed
on GPU.
Fig.1. Floating-point operations per second for the CPU and GPU
Yefimenko S.M.
Індуктивне моделювання складних систем, випуск 4, 2012 45
Fig.2. Memory bandwidth for the CPU and GPU
3 GMDH combinatorial algorithm
Let us consider the variants of computations organization in the combinatorial
generator. There are many schemes for change of binary structural vector, specifying
the sequence of regressors including in the model. Two of them (generally used) are
described below.
3.1 Scheme of algorithm with the use of binary numbers generator
The scheme uses generation of binary numbers, corresponding to sequential
decimal numbers. Complication of partial models changes from 1 to the maximal
number of m.
The scheme is simple enough and effective in case of uniprocessor system.
However it is not quite suitable for paralleling of combinatorial algorithm, because it
does not provide the even loading on every multiprocessor. The least computational
Optimal Paralleling for Solving Combinatorial Modelling Problems
Індуктивне моделювання складних систем, випуск 4, 2012 46
loading (larger common amount of arguments at the identical amount of models) will
fall on multiprocessors with a less sequence number, and most loading – on
multiprocessors with most sequence number, where models will be with the amount
of arguments, near to the number of m. It is related to the feature of structural vector
forming on principle of binary counter.
3.2 Scheme of algorithm with successive complication of structures
This scheme uses such sequence of binary numbers generation when at first all
connections appear with one unit in a structural vector ( mCm =1 possible variants),
then – with two units (
2
)1(2 −
=
mmCm possible variants), and etc to one possible
variant 1=m
mC of including in the model of all arguments.
Such scheme can be easily enough applied for parallelization of
combinatorial algorithm. Idea of the equal apportionment of common amount of
models and arguments on all processors of the cluster system consists in the
following. Amount of models
!)!(
!
iim
mCi
m ×−
= complexity of mii ,1, = , is evenly
distributed between all processors of p (i.e. every processor “handles”
!)!(
!
iimp
m
×−×
models). Thus, it is necessary to define an initial point (first
structural vector) for every processor.
4 Paralleling of GMDH combinatorial algorithm for GPU
We will consider the scheme of algorithm with successive complication of
structures of binary numbers generator. The corresponding scheme for paralleling on
CPU was constructed in [4].
The scheme of algorithm paralleling for determination of the initial state of bi-
nary structural vector by position for every multiprocessor is proposed later. Parallel-
ing of other parts for GMDH combinatorial algorithm using GPU, as well as using
cluster systems [2] presents no substantial difficulties.
Lets we have m arguments and к multiprocessors within GPU. We will write
down the sequence of operations for the models of complication mii ,1, = :
1. Calculation of amount of combinations – 1−i
mC .
Yefimenko S.M.
Індуктивне моделювання складних систем, випуск 4, 2012 47
2. Determination of the initial state of binary vector d for every multiproces-
sor kjj ,1, = , as a decimal number 1)1(
1
+−
⎥
⎥
⎦
⎤
⎢
⎢
⎣
⎡ −
j
k
C i
m .
3. Conversion from the decimal number to appropriate binary number for eve-
ry multiprocessor:
position = 1)1(
1
+−
⎥
⎥
⎦
⎤
⎢
⎢
⎣
⎡ −
j
k
C i
m ;
u=i-1, d=m-1, u
dCC = ;
Cycle on mll ,1, =
if position<=C then b[l]=1, u= u -1, d= d -1, u
dCC = ;
else b[i]=0, position = position – С, u= u -1, u
dCC = .
Conclusion
The principle possibility for the use of graphics processing units for solving
combinatorial modelling problems is shown. Scheme of operations paralleling using
GPU in a combinatorial algorithm on principle of binary counter is proposed. The
scheme provides the uniform loading on all multiprocessors of GPU. Further investi-
gations will be devoted to comparative testing of combinatorial algorithm paralleling
using GPU and cluster systems.
References
1. V. S. Stepashko, and S. N. Efimenko. Sequential Estimation of the
Parameters of Regression Model // Cybernetics and Systems Analysis, Springer New
York, July, 2005, Vol. 41, Num. 4, pp.631-634.
2. Stepashko V.S., Yefimenko S.M., Rozenblat O.P., Chernyack A.I. On
application of parallel computations in tasks of modelling on the basis of inductive
approach // Problems in programming. – 2006. – № 2-3. – PP. 170-176.
3. NVIDIA CUDA C Programming Guide, [Online]. Available:
http://developer.nvidia.com/nvidia-gpu-computing-documentation.
4. V. S. Stepashko, S. N. Efimenko. Optimal paralleling for solving
combinatorial modelling problems // Proceedings of the 2nd International Conference
on Inductive Modelling ICIM 2008. – Kyiv, 2008. – P. 172-175.
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| id | nasplib_isofts_kiev_ua-123456789-45957 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | XXXX-0044 |
| language | English |
| last_indexed | 2025-11-27T11:05:42Z |
| publishDate | 2012 |
| publisher | Міжнародний науково-навчальний центр інформаційних технологій і систем НАН та МОН України |
| record_format | dspace |
| spelling | Yefimenko, S. 2013-06-21T08:31:33Z 2013-06-21T08:31:33Z 2012 Optimal Paralleling for Solving Combinatorial Modelling Problems using Graphics Processing Units / S. Yefimenko // Індуктивне моделювання складних систем: Зб. наук. пр. — К.: МННЦ ІТС НАН та МОН України, 2012. — Вип. 4. — С. 43-47. — Бібліогр.: 4 назв. — англ. XXXX-0044 https://nasplib.isofts.kiev.ua/handle/123456789/45957 519.254 The paper considers possibility of combinatorial GMDH algorithm computational speedup by means of programs paralleling for computing on graphics processing units. The scheme of algorithm with successive complication of structures providing the uniform loading on all multiprocessors of graphic card is proposed. У роботі розглядається можливість підвищення ефективності комбінаторного алгоритму МГУА за допомогою розпаралелювання обчислень на графічному процесорі. Запропоновано схему алгоритму з послідовним ускладненням структур, яка забезпечує рівномірне навантаження на всі мультипроцесори графічної карти. В работе рассматривается возможность повышения эффективности комбинаторного алгоритма МГУА с помощью распараллеливания вычислений на графическом процессоре. Предложена схема алгоритма с последовательным усложнением структур, обеспечивающая равномерную нагрузку на все мультипроцессоры графической карты. en Міжнародний науково-навчальний центр інформаційних технологій і систем НАН та МОН України Індуктивне моделювання складних систем Optimal Paralleling for Solving Combinatorial Modelling Problems using Graphics Processing Units Article published earlier |
| spellingShingle | Optimal Paralleling for Solving Combinatorial Modelling Problems using Graphics Processing Units Yefimenko, S. |
| title | Optimal Paralleling for Solving Combinatorial Modelling Problems using Graphics Processing Units |
| title_full | Optimal Paralleling for Solving Combinatorial Modelling Problems using Graphics Processing Units |
| title_fullStr | Optimal Paralleling for Solving Combinatorial Modelling Problems using Graphics Processing Units |
| title_full_unstemmed | Optimal Paralleling for Solving Combinatorial Modelling Problems using Graphics Processing Units |
| title_short | Optimal Paralleling for Solving Combinatorial Modelling Problems using Graphics Processing Units |
| title_sort | optimal paralleling for solving combinatorial modelling problems using graphics processing units |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/45957 |
| work_keys_str_mv | AT yefimenkos optimalparallelingforsolvingcombinatorialmodellingproblemsusinggraphicsprocessingunits |