Abstract
We present the Hogs and Slackers genetic algorithm (GA) which addresses the problem of improving the parallelization efficiency of sparse matrix computations by optimally distributing blocks of matrices data. The performance of a distribution is sensitive to the non-zero patterns in the data, the algorithm, and the hardware architecture. In a candidate distributions the Hogs and Slackers GA identifies processors with many operations – hogs, and processors with fewer operations – slackers. Its intelligent operation-balancing mutation operator then swaps data blocks between hogs and slackers to explore a new data distribution.We show that the Hogs and Slackers GA performs better than a baseline GA. We demonstrate Hogs and Slackers GA’s optimization capability with an architecture study of varied network and memory bandwidth and latency.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Biriukov, A., Ulyanov, D.: Simulation of parallel time-critical programs with the dynamo system. In: Proceedings of the Third IEEE Conference on Control Applications, pp. 825–829. IEEE Computer Society (1994), doi:10.1109/CCA.1994.381214
Bliss, N., Kepner, J.: pMatlab Parallel MATLAB Library. International Journal of High Performance Computing Applications (IJHPCA), Special Issue on High-Productivity Programming Languages and Models 21(3), 336–359 (2007)
Buluç, A., Gilbert, J.R.: Challenges and advances in parallel sparse matrix-matrix multiplication. In: The 37th International Conference on Parallel Processing (ICPP 2008), pp. 503–510. IEEE Computer Society (2008)
Buluç, A., Gilbert, J.R.: New ideas in sparse matrix-matrix multiplication. In: Kepner, J., Gilbert, J.R. (eds.) Graph Algorithms in the Language of Linear Algebra. SIAM Press (2008)
Chakrabarti, D., Zhan, Y., Faloutsos, C.: R-mat: A recursive model for graph mining. In: SIAM Data Mining SDM 2004 (2004)
D’Alberto, P., Nicolau, A.: R-kleene: A high-performance divide-and-conquer algorithm for the all-pair shortest path for densely connected networks. Algorithmica 47(2), 203–213 (2007)
Davis, T.A.: Direct Methods for Sparse Linear Systems. SIAM, Philadelphia (2006)
Filippone, S., Colajanni, M.: Psblas: a library for parallel linear algebra computation on sparse matrices. ACM Trans. Math. Softw. 26(4), 527–550 (2000)
Floyd, R.W.: Algorithm 97: Shortest path. Commun. ACM 5(6), 345 (1962)
Foo, S.K., Saratchandran, P., Sundararajan, N.: Genetic algorithm based pattern allocation schemes for training set parallelism in backpropagation neural networks. In: IEEE International Conference on Evolutionary Computation, pp. 545–550. IEEE Computer Society (1995), doi:10.1109/ICEC.1995.487442
Gilbert, J.R., Reinhardt, S., Shah, V.B.: A unified framework for numerical and combinatorial computing. Computing in Science and Engg. 10(2), 20–25 (2008)
Grefenstette, J.J.: Incorporating problem-specific knowledge into genetic algorithms. In: Davis, L. (ed.) Genetic Algorithms and Simulated Annealing, ch. 4, pp. 42–60. Morgan Kaufmann (1987)
Horn, R.A., Johnson, C.R.: Matrix Analysis. Cambridge University Press, Cambridge (1985)
Hosny, M.I., Mumford, C.L.: Single vehicle pickup and delivery with time windows: made to measure genetic encoding and operators. In: Proceedings of the 2007 Genetic and Evolutionary Computation Conference, GECCO 2007, pp. 2489–2496. ACM, New York (2007), http://doi.acm.org/10.1145/1274000.1274015 , doi:10.1145/1274000.1274015
Du, I.S., Erisman, A., Reid, J.K.: Direct Methods for Sparse Matrices. Oxford University Press, Oxford (1986)
Jose, A.: An approach to mapping parallel programs on hypercube multiprocessors. In: Proceedings of the Seventh Euromicro Workshop on Parallel and Distributed Processing, PDP 1999, pp. 221–225 (1999), doi:10.1109/EMPDP.1999.746675
Kalinowski, T.: Solving the mapping problem with a genetic algorithm on the maspar-1. In: Proceedings of the First International Conference on Massively Parallel Computing Systems, pp. 370–374. IEEE Computer Society (1994), doi:10.1109/MPCS.1994.367057
Kepner, J., Bliss, N., Robinson, E.: Linear algebraic graph algorithms for back end processing. In: Proceedings of Workshop on High Performance Embedded Computing, HPEC 2008 (2008)
Kuck, D.: High Performance Computing: Challenges for Future Systems. Oxford University Press, New York (1996)
Kwok, Y.K., Ahmad, I.: Static scheduling algorithms for allocating directed task graphs to multiprocessors. ACM Computing Surveys 31(4), 406–471 (1999), http://doi.acm.org/10.1145/344588.344618 , doi:10.1145/344588.344618
Laird, J.E., Newell, A.: A universal weak method: summary of results. In: IJCAI 1983: Proceedings of the Eighth International Joint Conference on Artificial intelligence, pp. 771–773. Morgan Kaufmann Publishers Inc., San Francisco (1983)
Lee, S., Eigenmann, R.: Adaptive runtime tuning of parallel sparse matrix-vector multiplication on distributed memory systems. In: ICS 2008: Proceedings of the 22nd Annual International Conference on Supercomputing, pp. 195–204. ACM, New York (2008)
Lin, W.Y.: Parallel sparse matrix ordering: quality improvement using genetic algorithms. In: Proceedings of the 1999 Congress on Evolutionary Computation, CEC 1999, pp. 2295–2301. IEEE Computer Society (1999), doi:10.1109/CEC.1999.785560
O’Reilly, U., Bliss, N., Mohindra, S., Mullen, J., Robinson, E.: Multi-objective optimization of sparse array computations. In: Proceedings of Workshop on High Performance Embedded Computing, HPEC 2009 (2009)
Rabin, M.O., Vazirani, V.V.: Maximum matchings in general graphs through randomization. J. Algorithms 10(4), 557–567 (1989)
Ramaswamy, S., Banerjee, P.: Automatic generation of efficient array redistribution routines for distributed memory multicomputers. In: Proceedings of the Fifth Symposium on the Frontiers of Massively Parallel Computation (Frontiers 1995). IEEE Computer Society (1995)
Reuther, A., Kepner, J., McCabe, A., Mullen, J., Bliss, N., Kim, H.: Technical challenges of supporting interactive HPC. In: HPCMP Users Group Conference, pp. 403–409. IEEE Computer Society (2007)
Robinson, E.: Array based betweenness centrality. In: SIAM Conference on Parallel Processing for Scientific Computing (2008)
Sadd, Y.: Iterative methods for sparse linear systems. SIAM, Philadelphia (2007)
Talbi, E.G., Muntean, T.: Hill-climbing, simulated annealing and genetic algorithms: a comparative study and application to the mapping problem. In: Proceeding of the Twenty-Sixth Hawaii International Conference on System Sciences, pp. 565–573. IEEE Computer Society (1993), doi:10.1109/HICSS.1993.284069
Tarjan, R.E.: A unified approach to path problems. J. ACM 28(3), 577–593 (1981)
Travinin, N., Hoffman, H., Bond, R., Chan, H., Kepner, J., Wong, E.: pMapper: Automatic mapping of parallel matlab programs. In: HPCMP Users Group Conference, pp. 254–261. IEEE Computer Society (2005)
Travinin Bliss, N., Mohindra, S., O’Reilly, U.: Performance modeling and mapping of sparse computations. In: HPCMP Users Group Conference, pp. 448–456. IEEE Computer Society (2008)
Xiong, K., Suh, S., Yang, M., Yang, J., Arabnia, H.: Next generation sequence analysis using genetic algorithms on multi-core technology. In: International Joint Conference on Bioinformatics, Systems Biology and Intelligent Computing (IJCBS 2009), pp. 190–191 (2009), doi:10.1109/IJCBS.2009.104
Yoo, A., Chow, E., Henderson, K., McLendon, W., Hendrickson, B., Catalyurek, U.: A scalable distributed parallel breadth-first search algorithm on BlueGene/L. In: Proceedings of the 2005 ACM/IEEE Conference on Supercomputing, SC 2005, p. 25. IEEE Computer Society, Washington, DC (2005)
Yuster, R., Zwick, U.: Detecting short directed cycles using rectangular matrix multiplication and dynamic programming. In: Proceedings of the Fifteenth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2004, pp. 254–260. Society for Industrial and Applied Mathematics, Philadelphia (2004)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer Berlin Heidelberg
About this chapter
Cite this chapter
O’Reilly, UM., Bliss, N., Mohindra, S., Mullen, J., Robinson, E. (2012). A Knowledge-Based Operator for a Genetic Algorithm which Optimizes the Distribution of Sparse Matrix Data. In: Fernández de Vega, F., Hidalgo Pérez, J., Lanchares, J. (eds) Parallel Architectures and Bioinspired Algorithms. Studies in Computational Intelligence, vol 415. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-28789-3_10
Download citation
DOI: https://doi.org/10.1007/978-3-642-28789-3_10
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-28788-6
Online ISBN: 978-3-642-28789-3
eBook Packages: EngineeringEngineering (R0)