Parallelization of Graceful Labeling Using Open MP
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This document summarizes research on parallelizing the graceful graph labeling problem using OpenMP on multi-core processors. It introduces the concepts of parallelization, multi-core architecture, and OpenMP. An algorithm is designed to parallelize graceful labeling by distributing graph vertices across processor cores. Execution time and speedup are measured for graphs of increasing size, showing improved speedup and reduced time with parallelization. Results show consistent performance gains as graph size increases due to better utilization of the multi-core architecture.
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Execution time – Time taken to execute the
program
The factor by which multi-core shows
improvement in finding solution is called speed up
the overall speedup S is given by the below
equation .
Speedup, S =
Tparallel
Tseries
Where,
Tserial – serial program execution time
Tparallel – parallel program execution time
No of
Vertices
Serial
Execution
Time(Micro
sec)
Parallel
Execution
Time(Micro
sec)
10*10
0412 0371
50*50
2313 2062
100*100
72501 65210
150*150
18751 16782
200*200
27983 26123
250*250
42516 41710
300*300
66543 61287
350*350
78142 60286
400*400
90421 84371
450*450
111242 107342
Table 1:Execution Time
Table 1 shows that for 10*10, there is no much
difference in execution time between serial and
parallel execution times. However, for 450*450,
there is a considerable amount of difference
between serial execution time and parallel
execution time. When the number of vertices
increases, the corresponding difference between
serial and parallel execution time also increases.
3. Speedup
The speedup is calculated by using the fraction of
code parallelized with speed obtained from serial
and parallel execution time which is shown in Table
2.
Table 2 Speedup
4. CONCLUSIONS
In this work, we learned how OpenMp
programming techniques are beneficial to multicore
systems. We also found out the execution time of
both serial and parallel programs. From the vertices
10 to 450, it shows consistent improvement. It is
concluded that by parallelization the speedup, and
execution time are improved.
.
5. REFERENCES
[1] Brankovic,&Wanless (2011). Graceful
Labelling: State of the Art, Applications and
Future Directions. Mathematics in
Computer Science, 5(1), 11–
20. doi:10.1007/s11786-011-0073-6
[2] Yamazaki ,Kurzak , Wu , Zounon ,
&Dongarra (2018). Symmetric Indefinite
Linear Solver Using OpenMP Task on
Multicore Architectures. IEEE Transactions
on Parallel and Distributed Systems, 29(8),
No of Vertices Speedup
10*10 1.112
50*50 1.121
100*100 1.123
150*150 1.125
200*200 1.125
250*250 1.123
300*300 1.127
350*350 1.130
400*400 1.134
450*450 1.148](https://image.slidesharecdn.com/ijsred-v3i5p23-200919143251/85/Parallelization-of-Graceful-Labeling-Using-Open-MP-3-320.jpg)
![Page 4
1879–
1892. doi:10.1109/tpds.2018.2808964
[3] Peipei , Tai , &Yuanyuan(2014). The
Generation of k-Graceful Figure and
Graceful Label.2014 Fourth International
Conference on Instrumentation and
Measurement, Computer, Communication
and Control. doi:10.1109/imccc.2014.94
[4] Zeng K, Tang Y, & Liu F
(2011). Parallization of Adaboost Algorithm
through Hybrid MPI/OpenMP and
Transactional Memory.2011 19th
International Euromicro Conference on
Parallel, Distributed and Network-Based
Processing. doi:10.1109/pdp.2011.97
[5] SheelaKathavate and N.K. Srinath,
Efficiency of Parallel Algorithms on
Multi Core Systems Using OpenMP,
International Journal of Advanced
Research in Computer and Communication
Engineering Vol. 3, Issue 10, October
2014.
[6] ChetanArora, Subhashis Banerjee,
PremKalra, and S.N. Maheshwari, An
Efficient GraphCut Algorithm for
Computer Vision Problems,
Department of Computer Science
and Engineering, Indian Institute of
Technology, New Delhi, India@Springer-
Verlag Berlin Heidelberg 2010.
[7] P.K.D Sridevi,A.Sindhuja,R.Muthuselvi
“Parallelization of maze generation and
solving in multicore Using
OpenMP” International Conference on
Innovations in Engineering and Technology,
ICIET 16, 6th and 7th April 2016 conducted
by KLN College of Engineering,Madurai.
[8] R.Muthuselvi, M.Muneeswari, K.Sudha,
V.Vasantha “Parallelization of Graph
Labelling Problem in Multicore using
OpenMP” International Conference on
Trends in Electronics and Informatics ICEI
2017 May 11th
and 12th
2017 conducted by
SCAD Engineering College, Thirunelveli
[9] Rohit Chandra, Leonardo Dagum, Dave
Kohr, DrorMaydan, Jeff McDonald,
Ramesh Menon ' Parallel Programming in
OpenMP' ch.1-6, pp.1-249.
[10] J.A. Mac Dougall, M. Miller, Slamin and
W. D. Wallis,Vertexmagic total labelling og
graphs,Util,Math.,61(2002)3-4.
[11] K.A. Hawick, A. Leist and D.P. Playne,
Parallel Graph Component Labelling with GPUs
and CUDA,International Journal of Engineering
and Technology Vol.3,2014.
.](https://image.slidesharecdn.com/ijsred-v3i5p23-200919143251/85/Parallelization-of-Graceful-Labeling-Using-Open-MP-4-320.jpg)
Parallelization of Graceful Labeling Using Open MP
- 1. Page 1 K.Aravindh*,R.P.Santharuban**,S.Sanjay*** *(Computer Science and Engineering, Kamaraj College of Engineering and Technology Email: [email protected]) *(Computer Science and Engineering, Kamaraj College of Engineering and Technology Email: [email protected]) *(Computer Science and Engineering, Kamaraj College of Engineering and Technology Email: [email protected]) ----------------------------------------------************************--------------------------------------------- Abstract: Parallelization is the process used for reducing the time that provides an efficient result for the real time applications. Multi-core architecture is a general purpose processor that consists of multiple cores on the same die and can execute programs simultaneously and parallelization can be applied effectively. Though the multiple cores are available in multi-core architecture, only single core is utilized unless the programmer intervenes. It is very crucial to use the multi-cores effectively. There are many applications such as communication network addressing, X-Ray Crystallography, Radar Communication, Astronomy and Circuit design which use graceful graph labelling problem for finding solutions. In real time, solving graceful graph labelling problem is time consuming process when numbers of nodes are processed sequentially. In this work, parallelization is applied to the Graceful Graph labelling problem in multi-core using OpenMP. It is found that speedup and execution time are reduced. After parallelization, the speed up is constantly improved as the size of the graph becomes large. Keywords — Multi-core, OpenMP, Graceful, Graph Labelling, Speedup, Execution Time . ---------------------------------------------************************---------------------------------------------- 1. INTRODUCTION The program which uses a large number of data as an input takes more time for the execution. This issue in the execution is because of the serial execution of the program. To avoid this issue the proposed system uses the OpenMP to execute the program in a parallel way. Parallelization is the act of designing a computer program or system to process data in parallel. Normally, computer programs compute data serially. They solve one problem, and then the next, then the next. If a computer program or system is parallelized, it breaks a problem down into smaller pieces that can each independently be solved at the same time by discrete computing resources. When optimized for this type of computation, parallelized programs can arrive at a solution much faster than programs executing processes in serial. Parallel processing is the method of evenly distributing computer processes between two or more computer processors. This requires a computer with multiple CPUs, or a CPU (or GPU) equipped with multiple cores. It also requires an operating system capable of supporting parallel processing, or software written specifically to process tasks in parallel. Parallel processing is the method of evenly distributing computer processes between two or more computer processors. Each new generation of processors approaches the physical limitations of microelectronics, which is a major engineering concern in CPU design. Parallelization of graceful labeling using OpenMP
- 2. Page 2 Because individual chips are approaching their fastest possible speeds, parallel processing becomes an important area in which to improve computing performance. The majority of modern desktop computers and laptops have multiple cores on their CPU that help parallel processing in the operating system. . 1.2 Multi-core Architecture Multi-core refers to an architecture in which a single physical processor incorporates the core logic of more than one processor. Multi-core architecture places multiple cores and bundles them as a single physical processor. The objective is to create a system that can complete more tasks at the same time, thereby gaining better overall system architecture A single integrated circuit is used to package or hold these processors. These single integrated circuits are known as a die. Multi-core architecture consists of multiple cores on the same die and can execute programs simultaneously, thereby gaining better overall system performance. The processing tasks are divided into sub tasks and assigned to different cores. At the time of task completion, the processed data from each core is collected and combined. This technique significantly enhances performance compared to a single- core processor of similar speed. 1.3 OpenMP Open MP stands for open multi-processing. OpenMP uses a portable, scalable model that gives programmers a simple and flexible interface for developing parallel applications for platforms ranging from the standard desktop computer to the supercomputer. Open MP is an application programming interface (API) that supports multi-platform shared memory multi- processing programming in C, C++, and Fortran, on many platforms, instruction set architectures and operating systems, including Solaris, , Linux, macOS, and Windows. OpenMP consists of a set of compiler directives, library routines, and environment variables. OpenMP is an implementation of multithreading, forks a specified number of slave threads and the system divides a task among them. The threads then run concurrently, with the runtime environment allocating threads to different processors. 3. System Design Fig 1:System Design This system is designed in such a way that to parallelize the graph labelling for different inputs. Normally, a graph consists of number of vertices and edges. The system accepts the edges and vertices as an input. The labelling can be calculated by finding the difference between the adjacent vertices. The checking of alpha labelling is performed. These processes are parallelized. Speedup is calculated based on the time taken for the execution of both serial and parallel program. The results are compared and analysed. 2. Execution Time In this module, the execution time to find out the weight for the graph is calculated by using equation. ( )( ) secondperClocks beginendfloat timeExecution − = Where, Begin-time at which program execution starts End-time at which program execution ends
- 3. Page 3 Execution time – Time taken to execute the program The factor by which multi-core shows improvement in finding solution is called speed up the overall speedup S is given by the below equation . Speedup, S = Tparallel Tseries Where, Tserial – serial program execution time Tparallel – parallel program execution time No of Vertices Serial Execution Time(Micro sec) Parallel Execution Time(Micro sec) 10*10 0412 0371 50*50 2313 2062 100*100 72501 65210 150*150 18751 16782 200*200 27983 26123 250*250 42516 41710 300*300 66543 61287 350*350 78142 60286 400*400 90421 84371 450*450 111242 107342 Table 1:Execution Time Table 1 shows that for 10*10, there is no much difference in execution time between serial and parallel execution times. However, for 450*450, there is a considerable amount of difference between serial execution time and parallel execution time. When the number of vertices increases, the corresponding difference between serial and parallel execution time also increases. 3. Speedup The speedup is calculated by using the fraction of code parallelized with speed obtained from serial and parallel execution time which is shown in Table 2. Table 2 Speedup 4. CONCLUSIONS In this work, we learned how OpenMp programming techniques are beneficial to multicore systems. We also found out the execution time of both serial and parallel programs. From the vertices 10 to 450, it shows consistent improvement. It is concluded that by parallelization the speedup, and execution time are improved. . 5. REFERENCES [1] Brankovic,&Wanless (2011). Graceful Labelling: State of the Art, Applications and Future Directions. Mathematics in Computer Science, 5(1), 11– 20. doi:10.1007/s11786-011-0073-6 [2] Yamazaki ,Kurzak , Wu , Zounon , &Dongarra (2018). Symmetric Indefinite Linear Solver Using OpenMP Task on Multicore Architectures. IEEE Transactions on Parallel and Distributed Systems, 29(8), No of Vertices Speedup 10*10 1.112 50*50 1.121 100*100 1.123 150*150 1.125 200*200 1.125 250*250 1.123 300*300 1.127 350*350 1.130 400*400 1.134 450*450 1.148
- 4. Page 4 1879– 1892. doi:10.1109/tpds.2018.2808964 [3] Peipei , Tai , &Yuanyuan(2014). The Generation of k-Graceful Figure and Graceful Label.2014 Fourth International Conference on Instrumentation and Measurement, Computer, Communication and Control. doi:10.1109/imccc.2014.94 [4] Zeng K, Tang Y, & Liu F (2011). Parallization of Adaboost Algorithm through Hybrid MPI/OpenMP and Transactional Memory.2011 19th International Euromicro Conference on Parallel, Distributed and Network-Based Processing. doi:10.1109/pdp.2011.97 [5] SheelaKathavate and N.K. Srinath, Efficiency of Parallel Algorithms on Multi Core Systems Using OpenMP, International Journal of Advanced Research in Computer and Communication Engineering Vol. 3, Issue 10, October 2014. [6] ChetanArora, Subhashis Banerjee, PremKalra, and S.N. Maheshwari, An Efficient GraphCut Algorithm for Computer Vision Problems, Department of Computer Science and Engineering, Indian Institute of Technology, New Delhi, India@Springer- Verlag Berlin Heidelberg 2010. [7] P.K.D Sridevi,A.Sindhuja,R.Muthuselvi “Parallelization of maze generation and solving in multicore Using OpenMP” International Conference on Innovations in Engineering and Technology, ICIET 16, 6th and 7th April 2016 conducted by KLN College of Engineering,Madurai. [8] R.Muthuselvi, M.Muneeswari, K.Sudha, V.Vasantha “Parallelization of Graph Labelling Problem in Multicore using OpenMP” International Conference on Trends in Electronics and Informatics ICEI 2017 May 11th and 12th 2017 conducted by SCAD Engineering College, Thirunelveli [9] Rohit Chandra, Leonardo Dagum, Dave Kohr, DrorMaydan, Jeff McDonald, Ramesh Menon ' Parallel Programming in OpenMP' ch.1-6, pp.1-249. [10] J.A. Mac Dougall, M. Miller, Slamin and W. D. Wallis,Vertexmagic total labelling og graphs,Util,Math.,61(2002)3-4. [11] K.A. Hawick, A. Leist and D.P. Playne, Parallel Graph Component Labelling with GPUs and CUDA,International Journal of Engineering and Technology Vol.3,2014. .