On the shortest linear straight-line program for computing linear forms

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 5162 LNCS, Issue , 2008, Pages 168-179

  Boyar, Joan ^a   Matthews, Philip ^a   Peralta, René ^b  

^a UNIVERSITY OF SOUTHERN DENMARK   (Denmark)

^b US ARMY ENGINEER RESEARCH AND DEVELOPMENT CENTER   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION RATIOS; COMPUTING; CRYPTOGRAPHIC APPLICATIONS; DECISION PROBLEMS; LINEAR OPERATIONS; LINEAR PROGRAMS; NP-HARD; OPTIMAL SOLUTIONS;

APPROXIMATION ALGORITHMS; COMPUTER SCIENCE; COMPUTERS; CRYPTOGRAPHY; FOUNDATIONS; NUCLEAR PROPULSION;

LINEAR PROGRAMMING;

EID: 54249141019     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-540-85238-4_13     Document Type: Conference Paper

References (12)

1. Arora, S., Lund, C., Motwani, R., Sudan, M., Szegedy, M.: Proof verification and the hardness of approximation problems. Journal of the Association for Computing Machinery 45, 501-555 (1998)
2. Blum, L., Shub, M., Smale, S.: On a theory of computation and complexity over the real numbers: NP-completeness, recursive functions and universal machines. Bull. Amer. Math. Soc. 21, 1-46 (1989)
3. Boyar. J., Peralta, R.: On building small circuits (2008) (manuscript in preparation)
4. Clementi, A.E.F., Trevisan, L.: Improved non-approximability results for vertex cover with density constraints. In: Computing and Combinatorics, pp. 333-342 (1996)
5. Cooley, J.W., Tukey, J.W.: An algorithm for the machine calculation of complex Fourier series. Math. Comp. 19, 297-301 (1965)
6. Håstad, J.: Tensor rank is NP-Complete. J. Algorithms 11(4), 644-654 (1990)
7. S̃hokrollahi, M.A., B̃ürgisser, P., Clausen, M.: Algebraic Complexity Theory, ch. 13. Springer, Heidelberg (1997)
8. Papadimitriou, C., Yannakakis, M.: Optimization, approximation, and complexity classes. Journal of Computer and System Sciences 43, 425-440 (1991)
9. Savage, J.E.: An algorithm for the computation of linear forms. SICOMP 3(2), 150-158 (1974)
10. Valiant, L.G.: Completeness classes in algebra. In: Proceedings of the 11th Annual ACM Symposium on the Theory of Computing, pp. 249-261 (1979)
11. Williams, R.: Matrix-vector multiplication in sub-quadratic time (some preprocessing required). In: Proceedings of the Eighteenth Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 995-1001 (2007)
12. Winograd, S.: On the number of multiplications necessary to compute certain functions. Comm. Pure and Applied Math. 23, 165-179 (1970)