Compressed matrix multiplication

ITCS 2012 - Innovations in Theoretical Computer Science Conference

Volumn , Issue , 2012, Pages 442-451

  Pagh, Rasmus ^a  

^a IT UNIVERSITY OF COPENHAGEN   (Denmark)

Author keywords

[No Author keywords available]

Indexed keywords

ERROR CORRECTING CODE; FROBENIUS NORM; MATRIX MULTIPLICATION; MATRIX PRODUCTS; NEAR-LINEAR TIME; NONZERO ENTRIES; POLYNOMIAL MULTIPLICATION; REAL MATRICES; SAMPLE COVARIANCES; SIMPLE ALGORITHM; UNBIASED ESTIMATOR;

APPROXIMATION ALGORITHMS; COMPUTER SCIENCE; HASH FUNCTIONS; INNOVATION;

COVARIANCE MATRIX;

EID: 84856478713     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1145/2090236.2090271     Document Type: Conference Paper

References (25)

1. Noga Alon, Phillip B. Gibbons, Yossi Matias, and Mario Szegedy. Tracking join and self-join sizes in limited storage. J. Comput. Syst. Sci, 64(3):719-747, 2002.
2. Noga Alon, Yossi Matias, and Mario Szegedy. The space complexity of approximating the frequency moments. J. Comput. Syst. Sci, 58(1):137-147, 1999.
3. Rasmus Resen Amossen, Andrea Campagna, and Rasmus Pagh. Better size estimation for sparse matrix products. In Proceedings of 13th International Workshop on Approximation, Randomization, and Combinatorial Optimization (APPROX-RANDOM), volume 6302 of Lecture Notes in Computer Science, pages 406-419. Springer, 2010.
4. Rasmus Resen Amossen and Rasmus Pagh. Faster join-projects and sparse matrix multiplications. In Proceedings of 12th International Conference on Database Theory (ICDT), volume 361 of ACM International Conference Proceeding Series, pages 121-126. ACM, 2009.
5. Vladimir Braverman, Kai-Min Chung, Zhenming Liu, Michael Mitzenmacher, and Rafail Ostrovsky. AMS without 4-wise independence on product domains. In 27th International Symposium on Theoretical Aspects of Computer Science (STACS), volume 5 of Leibniz International Proceedings in Informatics (LIPIcs), pages 119-130, 2010.
6. J. Lawrence Carter and Mark N. Wegman. Universal classes of hash functions. Journal of Computer and System Sciences, 18(2):143{154, 1979.
7. Moses Charikar, Kevin Chen, and Martin Farach-Colton. Finding frequent items in data streams. Theor. Comput. Sci, 312(1):3-15, 2004.
8. Kenneth L. Clarkson and David P. Woodruff. Numerical linear algebra in the streaming model. In Proceedings of Symposium on Theory of Computing (STOC), pages 205-214. ACM Press, 2009.
9. Edith Cohen. Structure prediction and computation of sparse matrix products. J. Comb. Optim, 2(4):307-332, 1998.
10. Edith Cohen and David D. Lewis. Approximating matrix multiplication for pattern recognition tasks.Journal of Algorithms, 30(2):211-252, 1999.
11. James W. Cooley and John W. Tukey. An algorithm for the machine calculation of complex Fourier series. Mathematics of Computation, 19(90):297-301, 1965.
12. Don Coppersmith and Shmuel Winograd. Matrix multiplication via arithmetic progressions. Journal of Symbolic Computation, 9(3):251-280, 1990.
13. Martin Dietzfelbinger, Joseph Gil, Yossi Matias, and Nicholas Pippenger. Polynomial hash functions are reliable (extended abstract). In Werner Kuich, editor,Automata, Languages and Programming, 19th International Colloquium, volume 623 of Lecture Notes in Computer Science, pages 235{246, Vienna, Austria,13{17 July 1992. Springer-Verlag.
14. Petros Drineas, Ravi Kannan, and Michael W.Mahoney. Fast Monte Carlo algorithms for matrices I:Approximating matrix multiplication. SIAM Journal on Computing, 36(1):132-157, 2006.
15. A. Gilbert and P. Indyk. Sparse recovery using sparse matrices. Proceedings of the IEEE, 98(6):937 {947, 2010.
16. Anna C. Gilbert, Yi Li, Ely Porat, and Martin J. Strauss. Approximate sparse recovery: optimizing time and measurements. In Proceedings of the 42nd ACM symposium on Theory of computing, STOC '10, pages 475-484, New York, NY, USA, 2010. ACM.
17. Leo A. Goodman. On the exact variance of products. Journal of the American Statistical Association, 55(292):pp. 708-713, 1960.
18. Piotr Indyk and Andrew McGregor. Declaring independence via the sketching of sketches. In Proceedings of the 19th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), pages 737-745. SIAM, 2008.
19. Mark A. Iwen and Craig V. Spencer. A note on compressed sensing and the complexity of matrix multiplication. Inf. Process. Lett, 109(10):468-471, 2009.
20. Andrzej Lingas. A fast output-sensitive algorithm for boolean matrix multiplication. In ESA, volume 5757 of Lecture Notes in Computer Science, pages 408-419. Springer, 2009.
21. Michael W. Mahoney. Algorithmic and statistical perspectives on large-scale data analysis, October 08 2010. To appear in Combinatorial Scientific Computing, Chapman and Hall/CRC Press, 2011.
22. Mihai Pǎ;traşcu and Mikkel Thorup. The power of simple tabulation hashing. In Proceedings of the 43rd annual ACM Symposium on Theory of Computing (STOC), pages 1-10. ACM, 2011.
23. Tamás Sarlós. Improved approximation algorithms for large matrices via random projections. In IEEE Symposium on Foundations of Computer Science (FOCS), pages 143-152. IEEE Computer Society, 2006.
24. Michael Sipser and Daniel A. Spielman. Expander codes. IEEE Transactions on Information Theory, 42(6):1710-1722, 1996.
25. Raphael Yuster and Uri Zwick. Fast sparse matrix multiplication. ACM Transactions on Algorithms, 1(1):2-13, 2005.