Matrix-vector multiplication in sub-quadratic time (some preprocessing required)

Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms

Volumn 07-09-January-2007, Issue , 2007, Pages 995-1001

  Williams, Ryan ^a  

^a Carnegie Mellon University   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

MATRIX VECTOR MULTIPLICATION; N-MATRIX; POINTER MACHINES; QUADRATIC TIME; SEMI-RING; VECTOR MULTIPLICATION;

ALGORITHMS;

EID: 84969234352     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (20)

1. [AHU74] A.V. Aho, J.E. Hopcroft, and J.D. Ullman. The Design and Analysis of Computer Algorithms. Addison-Wesley, Reading, MA, 1974.
2. [ADKF70] V.Z. Arlazarov, E.A. Dinic, M.A. Kronrod and I.A. Faradzev. On economical construction of the transitive closure of a directed graph. Doklady Adamedii Nauk SSSR 194:487-488, 1970.
3. [AS88] M.D. Atkinson and N. Santoro. A practical algorithm for Boolean matrix multiplication. Inf. Proc. Letters 29:37-38, 1988.
4. [BKM95] J. Basch, S. Khanna, and R. Motwani. On Diameter Verification and Boolean Matrix Multiplication. Technical Report No. STAN-CS-95-1544, Department of Computer Science, Stanford University, 1995.
5. [BM75] A. Borodin and I. Munro. The Computational Complexity of Algebraic and Numerical Problems. Elsevier, New York, 1975.
6. 3/log n) Time. Proc. Workshop on Algorithms and Data Structures (WADS), 318-324, 2005.
7. [C06] T.M. Chan. All-Pairs Shortest Paths for Unweighted Undirected Graphs in o(mn) Time. Proc. ACM-SIAM Symposium on Discrete Algorithms (SODA), 514-523, 2006.
8. [CW90] D. Coppersmith and S. Winograd. Matrix Multiplication via Arithmetic Progressions. J. Symb. Comput. 9(3):251-280, 1990.
9. [F72] C.M. Fiduccia. Polynomial evaluation via the division algorithm-the Fast Fourier Transform revisited. Proc. ACM Symposium on Theory of Computing (STOC), 88-93, 1972.
10. [GO94] I. Gohberg and V. Olshevsky. Fast algorithms with preprocessing for matrix-vector multipication problems. Journal of Complexity 10(4):411-427, 1994.
11. [M55] T.S. Motzkin. Evaluation of polynomials and evaluation of rational functions. Bulletin of American Mathematical Society Vol. 61, 163, 1955.
12. [MB72] R. Moenck and A. Borodin. Fast modular transforms via division. Proc. IEEE 13th Annual Symposium on Switching and Automata Theory, 90-96, 1972.
13. [OS00] V. Olshevsky and A. Shokrollahi. Matrix-vector product for confluent Cauchy-like matrices with application to confluent rational interpolation. Proc. ACM Symposium on Theory of Computing (STOC), 573-581, 2000.
14. [P00] V.Y. Pan. Nearly optimal computations with structured matrices. Proc. ACM-SIAM Symposium on Discrete Algorithms (SODA), 953-962, 2000.
15. [P01] V.Y. Pan. Structured Matrices and Polynomials: Unified Superfast Algorithms. Birkhäuser-Springer, Boston and New York, 2001.
16. [R85] W. Rytter. Fast Recognition of Pushdown Automaton and Context-free Languages. Information and Control 67(1-3):12-22, 1985.
17. [S74] J.E. Savage. An algorithm for the computation of linear forms. SIAM J. Comput. 3(2):150-158, 1974.
18. [S80] N. Santoro. Extending the Four Russians' Bound to General Matrix Multiplication. Inf. Proc. Letters 10(2):87-88, 1980.
19. [S69] V. Strassen. Gaussian elimination is not optimal. Numer. Math. 12:354-356, 1969.
20. [W70] S. Winograd. On the number of multiplications necessary to compute certain functions. Comm. Pure and Applied Math. 23:165-179, 1970.