Time-space trade-off lower bounds for randomized computation of decision problems

Journal of the ACM

Volumn 50, Issue 2, 2003, Pages 154-195

  Beame, Paul ^a   Saks, Michael ^b   Sun, Xiaodong ^b,c   Vee, Erik ^a  

^a UNIVERSITY OF WASHINGTON   (United States)

^b RUTGERS UNIVERSITY   (United States)

^c INSTITUTE FOR ADVANCED STUDY   (United States)

Author keywords

Branching programs; Element distinctness; Quadratic forms; Random access machines

Indexed keywords

BRANCHING PROGRAMS; ELEMENT DISTINCTNESS; QUADRATIC FORMS; RANDOM-ACCESS MACHINES;

BOOLEAN ALGEBRA; COMPUTATIONAL COMPLEXITY; COMPUTATIONAL METHODS; PARAMETER ESTIMATION; PROBLEM SOLVING; RANDOM ACCESS STORAGE;

DECISION THEORY;

EID: 4243063946     PISSN: 00045411     EISSN: None     Source Type: Journal    
DOI: 10.1145/636865.636867     Document Type: Article

References (29)

1. ABRAHAMSON, K. R. 1990. A time-space tradeoff for Boolean matrix multiplication. In Proceedings 31st Annual Symposium on Foundations of Computer Science. (St. Louis, Mo.) IEEE Computer Society Press, Los Alamitos, Calif., 412-419.
2. ABRAHAMSON, K. R. 1991. Time-space trade-offs for algebraic problems on general sequential models. J. Comput. Syst. Sci. 43, 2 (Oct.), 269-289.
3. AJTAI, M. 1999a. Determinism versus non-determinism for linear time RAMs with memory restrictions. In Proceedings of the 31st Annual ACM Symposium on Theory of Computing (Atlanta, Ga.). ACM, New York, 632-641.
4. AJTAI, M. 1999b. A non-linear time lower bound for boolean branching programs. In Proceedings 40th Annual Symposium on Foundations of Computer Science (New York, N.Y.) IEEE Computer Society Press, Los Alamitos, Calif., 60-70.
5. AJTAI, M. 2002. Determinism versus non-determinism for linear time RAMs with memory restrictions. J. Comput. Syst. Sci. 65, 1 (Aug.), 2-37.
6. ALON,N., AND MAASS, W. 1988. Meanders and their applications in lower bounds arguments. J. Comput. Syst. Sci. 37, 118-129.
7. BASAI, L., FRANKL, P., AND SIMON, J. 1986. Complexity classes in communication complexity theory. In Proceedings of the 27th Annual Symposium on Foundations of Computer Science. (Toronto, Ontario, Canada). IEEE Computer Society Press, Los Alamitos, Calif., 337-347.
8. BABAI, L., NISAN, N., AND SZEOEDY, M. 1992. Multiparty protocols, pseudorandom generators for logspace, and time-space trade-offs. J. Comput. Syst. Sci. 45, 2 (Oct.), 204-232.
9. BEAME, P., JAYRAM, T.S., AND SAKS, M. 2001. Time-space trade-offs for branching programs. J. Comput. Syst. Sci. 63, 4 (Dec.), 542-572.
10. BEAME, P., AND VEE, E. 2002. Time-space trade-offs, multiparty communication complexity, and nearest-neighbor problems. In Proceedings of the 34th Annual ACM Symposium on Theory of Computing, (Montreal, Quebec, Canada). ACM, New York, 688-697.
11. BEAME, P. W. 1991. A general time-space tradeoff for finding unique elements. SIAM J. Comput. 20, 2, 270-277.
12. BEAME, P. W., SAKS, M., AND THATHACHAR, J. S. 1998. Time-space trade-offs for branching programs. In Proceedings 39th Annual Symposium on Foundations of Computer Science (Palo Alto, Calif.). IEEE Computer Society Press, Los Alamitos, Calif., 254-263.
13. BORODIN, A. 1993. Time space trade-offs (getting closer to the barrier?). In Proceedings of the 4th International Symposium on Algorithms and Computation (Hong Kong). 209-220.
14. BORODIN, A., AND COOK, S. A. 1982. A time-space tradeoff for sorting on a general sequential model of computation. SIAM Journal on Computing 11, 2 (May), 287-297.
15. BORODIN, A., FICH, F. E., MEYER AUF DER HEIDE, F., UPFAL, E., AND WIGDERSON, A. 1987. A time-space tradeoff for element distinctness. SIAM J. Comput. 16, 1 (Feb.), 97-99.
16. BORODIN, A., FISCHER, M. J., KIRKPATRICK, D. G., LYNCH, N. A., AND TOMPA, M. 1981. A time-space tradeoff for sorting on non-oblivious machines. J. Comput. Syst. Sci. 22, 3 (June), 351-364.
17. BORODIN, A., RAZBOROV, A. A., AND SMOLENSKY, R. 1993. On lower bounds for read-k times branching programs. Comput. Complex. 3, 1-18.
18. FORTNOW, L. 1997. Nondeterministic polynomial time versus nondeterministic logarithmic space: Time-space trade-offs for satisfiability. In Proceedings of the 12th Annual IEEE Conference on Computational Complexity (formerly: Structure in Complexity Theory Conference) (Ulm, Germany) IEEE Computer Society Press, Los Alamitos, Calif, 52-60.
19. FORTNOW, L., AND VAN MELKEBEEK, D. 2000. Time-space trade-offs for nondeterministic computation. In Proceedings of the 15th Annual IEEE Conference on Computational Complexity (Florence, Italy,) IEEE Computer Society Press, Los Alamitos, Calif., 2-13.
20. HARDY, G. H., LITTLEWOOD, J. E., AND POLYA, G. 1952. Inequalities. Cambridge University Press.
21. HARPER, L. 1966. Optimal numberings and isoperimetric problems on graphs. 1, Combinat. Theory 1, 385-394.
22. KALYANASUNDARAM, B., AND SCHNITGER, G. 1987. The probabilistic communication complexity of set intersection. In Proceedings, 2nd Annual Conference on Structure in Complexity Theory, (Cornell University, Ithaca, N.Y.) IEEE Computer Society Press, Los Alamitos, Calif., 41-49.
23. KUSHILEVITZ, E., AND NISAN, N. 1997. Communication Complexity. Cambridge University Press, Cambridge [England]: New York.
24. LIPTON, R., AND VIOLAS, A. 1999. Time-space trade-offs for SAT. In Proceedings of the 40th Annual Symposium on Foundations of Computer Science (New York, N.Y.) IEEE Computer Society Press, Los Alamitos, Calif., 459-464.
25. MANSOUR, Y., NISAN, N., AND TIWARI, P. 1993. The computational complexity of universal hashing. Theoret. Comput. Sci. 107, 121-133.
26. OKOL' NISHNIKOVA, E. 1993. On lower bounds for branching programs. Sib. Adv. Math. 3, 1, 152-166.
27. PAGTER, J. 2001. Time-Space Tradeoffs. Ph.D. thesis, BRIGS.
28. RAZBOROV, A. A. 1990. On the distributional complexity of disjointness. In Automata, Languages, and Programming: 17th International Colloquium, (Warwick University, England). M. S. Paterson, Ed. Lecture Notes in Computer Science, vol. 443. Springer-Verlag, New York, 249-253.
29. YAO, A. C. 1988. Near-optimal time-space tradeoff for element distinctness. In Proceedings of the 29th Annual Symposium on Foundations of Computer Science (White Plains, N.Y.) IEEE Computer Society Press, Los Alamitos, Calif., 91-97.