Optimal Sparse Matrix Dense Vector Multiplication in the I/O-Model

Theory of Computing Systems

Volumn 47, Issue 4, 2010, Pages 934-962

  Bender, Michael A ^a   Brodal, Gerth Stølting ^b   Fagerberg, Rolf ^c   Jacob, Riko ^d   Vicari, Elias ^e  

^a Stony Brook University   (United States)

^b AARHUS UNIVERSITY   (Denmark)

^c UNIVERSITY OF SOUTHERN DENMARK   (Denmark)

^d TECHNICAL UNIVERSITY OF MUNICH   (Germany)

^e ETH ZURICH   (Switzerland)

Author keywords

External memory algorithms; I O model; Lower bound; Sparse matrix dense vector multiplication

Indexed keywords

AVERAGE NUMBERS; CONSTANT FACTORS; EXTERNAL MEMORY ALGORITHMS; LOWER BOUNDS; MODEL OF COMPUTATION; SPARSE MATRICES; VECTOR MULTIPLICATION; WORST-CASE COMPLEXITY;

ALGORITHMS;

VECTORS;

EID: 77956611313     PISSN: 14324350     EISSN: 14330490     Source Type: Journal    
DOI: 10.1007/s00224-010-9285-4     Document Type: Article

References (18)

1. Aggarwal, A., Vitter, J. S.: The input/output complexity of sorting and related problems. Commun. ACM 31(9), 1116-1127 (1988).
2. Arge, L., Miltersen, P. B.: On showing lower bounds for external-memory computational geometry problems. In: Abello, J. M., Vitter, J. S. (eds.) External Memory Algorithms and Visualization. DIMACS Series in Discrete Mathematics and Theoretical Computer Science, vol. 50, pp. 139-159. American Mathematical Society, Providence (1999).
3. Brodal, G. S., Fagerberg, R.: On the limits of cache-obliviousness. In: Proc. 35th Annual ACM Symposium on Theory of Computing (STOC), pp. 307-315. ACM, San Diego (2003).
4. Brodal, G. S., Fagerberg, R., Moruz, G.: Cache-aware and cache-oblivious adaptive sorting. In: Proc. 32nd International Colloquium on Automata, Languages, and Programming. Lecture Notes in Computer Science, vol. 3580, pp. 576-588. Springer, Berlin (2005).
5. Cormen, T. H., Sundquist, T., Wisniewski, L. F.: Asymptotically tight bounds for performing BMMC permutations on parallel disk systems. SIAM J. Comput. 28(1), 105-136 (1999).
6. Demmel, J., Dongarra, J., Eijkhout, V., Fuentes, E., Antoine Petitet, R. V., Whaley, R. C., Yelick, K.: Self-adapting linear algebra algorithms and software. Proc. IEEE 93(2) (2005). Special Issue on Program Generation, Optimization, and Adaptation.
7. Filippone, S., Colajanni, M.: PSBLAS: a library for parallel linear algebra computation on sparse matrices. ACM Trans. Math. Softw. 26(4), 527-550 (2000).
8. Frigo, M., Leiserson, C. E., Prokop, H., Ramachandran, S.: Cache-oblivious algorithms. In: Proc. 40th Annual Symposium on Foundations of Computer Science (FOCS), pp. 285-297. IEEE Computer Society, New York (1999).
9. Hong, J.-W., Kung, H. T.: I/O complexity: the red-blue pebble game. In: Proc. 13th Annual ACM Symposium on Theory of Computing (STOC), pp. 326-333. ACM, New York (1981).
10. Im, E. J.: Optimizing the performance of sparse matrix-vector multiplication. PhD thesis, University of California, Berkeley, May 2000.
11. Raz, R.: Multi-linear formulas for permanent and determinant are of super-polynomial size. In: Proc. 36th Annual ACM Symposium on Theory of Computing (STOC), Chicago, IL, USA, pp. 633-641. ACM, New York (2004).
12. Remington, K., Pozo, R.: NIST sparse BLAS user's guide. Technical report, National Institute of Standards and Technology, Gaithersburg, MD (1996).
13. Saad, Y.: Sparsekit: a basic tool kit for sparse matrix computations. Technical report, Computer Science Department, University of Minnesota, June 1994.
14. Strassen, V.: Gaussian elimination is not optimal. Numer. Math. 13(4), 354-356 (1969).
15. Toledo, S.: A survey of out-of-core algorithms in numerical linear algebra. In: Abello, J. M., Vitter, J. S. (eds.) External Memory Algorithms and Visualization. DIMACS Series in Discrete Mathematics and Theoretical Computer Science, vol. 50, pp. 161-179. American Mathematical Society, Providence (1999).
16. Vitter, J. S.: External memory algorithms and data structures. In: Abello, J. M., Vitter, J. S. (eds.) External Memory Algorithms and Visualization. DIMACS Series in Discrete Mathematics and Theoretical Computer Science, vol. 50 pp. 1-38. American Mathematical Society, Providence (1999).
17. Vudac, R., Demmel, J. W., Yelick, K. A.: The Optimized Sparse Kernel Interface (OSKI) library: user's guide for version 1. 0. 1b. Berkeley Benchmarking and OPtimization (BeBOP) Group, 15 March 2006.
18. Vuduc, R. W.: Automatic performance tuning of sparse matrix kernels. PhD thesis, University of California, Berkeley, Fall 2003.