Parallel Merge Sort Using MPI
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1 Parallel Merge Sort Using MPI CSE 702: Seminar on Programming Massively Parallel Systems Course Instructor: Dr. Russ Miller UB Distinguished Professor Department of Computer Science & Engineering State University of New York at Buffalo Prepared By: Swati Nair UB Person Number:
2 Agenda Sequential Merge Sort Sequential Algorithm Analysis Proposed parallel algorithm Experimentation in CCR Obtained results and analysis Challenges Learning from the course Conclusion References 2
3 Sequential Merge Sort mergesort(int[] a, int left, int right) 1. If the input sequence has fewer than two elements, return 2. Partition the input sequence into two halves: mid = (left + right)/ 2 3. Sort the two subsequences using the same algorithm: mergesort(a, left, mid-1) mergesort(a,mid,right) 4. Merge the two sorted subsequences to form the output sequence Runtime: O(Nlog N) 3
4 Sequential Algorithm Analysis: Data Size Time taken by recursive solution (1M) Time in seconds 4
5 Proposed Parallel Algorithm Level = 3; Right child: 0 1<<2 Level = 2; Right child : 4 1<<1 Level = 1; Right child : 4 1<<1 Level = 0 1. To compute rank of right child: myrank (1<<(myHeight-1)) 2. To compute rank of parent: myrank & ~(1<<myHeight) => Needed to send the sorted data to parent node 5
6 Proposed Parallel Algorithm 1. Node with rank 0 is the host node. It computes the height of the node and get the entire dataset 2. Node 0 initiates the parallel merge operation 3. For internal nodes (height > 0) including node 0, a. Divide the data in half and send the right half to the right child as computed in previous slide b. Recursively call parallel merge operation for the left half on the same node c. Also, receive the sorted data from right child d. Merge the sorted left and right halves 4. If it is a leaf node, just do internal sorting 5. If parent s rank <> node s rank, send the sorted data to parent node 6. Finally, node 0 will have the entire sorted result 6
7 Experimentation in CCR 1. Allocation of nodes using salloc/sbatch script: salloc --nodes=8 --ntasks-per-node=1 --time=00:30:00 --exclusive Batch Script (in next slide) 2. Monitoring of submitted jobs: squeue -u swatishr 3. To check node availability sinfo 7
8 Experimentation in CCR: SBATCH script 8
9 Results 1. For some data size, plot processing time vs number of nodes a. Tested on 9 different data sizes: , , 1M, 2M, 4M, 8M, 100M, 200M, 1 billion (showing results for few of them) b. Number of nodes: 2, 4, 8, 16, 32, 64, 128, Plot speed-up that shows performance of parallel over sequential 3. Plot graphs that depict for a particular number of processor, how the runtime is affected with data size 9
10 Runtime Vs Number of nodes for N = Data Size: Processors Time
11 Runtime Vs Number of nodes for N = 1 million Key Size: (1 million) Processors Time
12 Runtime Vs Number of nodes for N = 2 million Key Size: (2 million) Processors Time
13 Runtime Vs Number of nodes for N = 8 million Key Size: (8 million) Processors Time
14 Runtime Vs Number of nodes for N = 200 million Key Size: (200 million) Processors Time
15 Runtime Vs Number of nodes for N = 1 billion Key Size: (1 billion) Processors Time
16 Speedup: Ratio of sequential to parallel execution time 16
17 Speedup for N = Baseline: Runtime on 1 node (Sequential): sec Key Size: Processors Speedup
18 Speedup for N = 8 million Baseline: Runtime on 1 node (Sequential): sec Key Size: 8 million Processors Speedup
19 Runtime Vs Data size (keeping number of processors constant) 19
20 Runtime Vs Data size for P = 2 and 256 Data size Time for 2 Processors Time for 256 Processors
21 Challenges & Learnings Long time to provision 128 and 256 nodes Analyzed the difference in runtimes as the number of nodes increased or as the data size increases Understood where parallelization should be used and how it can speed up the performance of sequential algorithms. Knowledge on MPI, CCR and Slurm jobs Use of different SLURM jobs such as sinfo, squeue, srun and salloc while troubleshooting node allocation. 21
22 Conclusion Only one task was associated with each node, thus, every physical server initiated one process only. According to the results, parallelism can be efficient only upto a particular number of processors/nodes. For further addition of nodes, network latency and/or size of smallest chunk of data hampers the performance! 22
23 References Dr. Russ Miller s webpage: Parallel Merge sort:
24 Thank you 24
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