Parallel bfs using 2 stacks
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This paper presents a hybrid parallel breadth-first search (BFS) algorithm for distributed memory systems that uses two stacks. BFS is important for graph algorithms and parallelizing it is important for large graphs. The paper's contributions include using a sparse matrix representation and a hybrid 1D partitioning approach. Experimental results on large systems show the 1D hybrid algorithm scales better than flat 1D partitioning for larger concurrencies and is up to 1.8 times faster than 2D partitioning algorithms. The paper concludes by conjecturing that level synchronous BFS can be implemented without errors using relaxed queues.
![Related Work: Level Synchronous Parallel BFS using 2
queues by Agarwal et al SC’10 [1]](https://image.slidesharecdn.com/parallel-bfs1-161002160500/85/Parallel-bfs-using-2-stacks-8-320.jpg)
Parallel bfs using 2 stacks
- 1. Parallel BFS on Distributed Memory Systems Aydin Buluc and Kamesh Madduri Sapta DC reading group September 29, 2016
- 2. Outline Introduction Shared Memory BFS Model Contributions Serial BFS overview Another paper: Parallel BFS using 2 queues This paper: Hybrid Parallel BFS using 2 stacks Experimental Results Conclusion
- 3. Introduction BFS is important. BFS usually forms a sub-part to more complex graph algorithms. Now that we have BIG graphs, parallelizing it is very important Shared Memory BFS involves: (1) communication between processors and (2) distribution of the graph(vertices) among processors
- 4. Model Graph G(V , E), and |V | = n and |E| = m, also m is O(n); i.e. sparse graphs. Edge weights = 1.
- 5. Contributions Traditional representation: 1 dimensional BFS (1D adjacency arrays). Sparse matrix representation: 2D partitioning of the graph (Not discussed).
- 6. Serial BFS overview Sequential BFS uses a queue data structure BFS requirement : all vertices at a distance k from the source should be “visited” before vertices at distance k + 1. Explanation? Level Synchronous BFS is a key concept in correct shared memory BFS.
- 7. Modified BFS : Use 2 stacks Can be parallelized as is: perform lines 6-7 in parallel, lines 8-10 are atomic
- 8. Related Work: Level Synchronous Parallel BFS using 2 queues by Agarwal et al SC’10 [1]
- 9. Hybrid 1D Parallel BFS Algorithm One of the main areas for optimization to this basic parallel algorithm is load-balancing: ensuring that parallelization of the edge visit steps is load-balanced 1D partitioning: If there are p processors in the system, give ownership of n/p vertices, to each processor. Random shuffling of the vertice identifiers prior to partitioning. So all processors ge roughly same number of vertices(n/p) and edges(m/p) Use of local stacks NSi for pushes and then global union.(Overhead < 3% of execution time)
- 10. 1D BFS
- 11. 1D BFS contd..
- 12. 1D BFS errors The value of level is not incremented The Next Stack NSi data structure should be emptied before traversing next level.
- 13. Experiments 1D Flat MPI: one process per core 1D Hybrid: one or more MPI processes within a node synthetic graphs based on the R-MAT random graph model(default m : n 16) , web crawl of the UK domain (133 million vertices and 5.5 billion edges). Systems: Hopper (6392-node Cray XE6) and Franklin (9660-node Cray XT4)
- 14. Experimental Results Strong scaling on Franklin Higher is better GTEPS: Giga Traversed Edges per Second
- 15. Experimental Results lower is better Strong scaling on Franklin
- 16. Experimental Results Weak Scaling on Franklin Lower is better
- 17. Experiments Flat 1D algorithms are about 1.5 − 1.8 times faster than the 2D algorithms. The 1D hybrid algorithm, are slower than the flat 1D algorithm for smaller concurrencies, starts to perform significantly faster for larger concurrencies.
- 18. Conclusion Conjecture: Level synchronous BFS can be implemented without any error with relaxed queues Question: Can the error be bounded if we don’t have a level synchronous algorithm?
- 19. V. Agarwal, F. Petrini, D. Pasetto, and D.A. Bader. Scalable graph exploration on multicore processors. In Proc. ACM/IEEE Conference on Supercomputing (SC10), November 2010. A. Buluc K. Madduri. Parallel breadth-first search on distributed memory systems. In Proceedings of 2011 International Conference for High Performance Computing, Networking, Storage and Analysis, SC ’11, pages 65:1–65:12, New York, NY, USA, 2011. ACM. C.E. Leiserson and T.B. Schardl. A work-efficient parallel breadth-first search algorithm (or how to cope with the nondeterminism of reducers). In Proc. 22nd ACM Symp. on Parallism in Algorithms and Architectures (SPAA ’10), pages 303–314, June 2010.
- 20. Thank You :)