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Time space tradeoffs (getting closer to the barrier?)

  • Session 5 Invited Paper
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Algorithms and Computation (ISAAC 1993)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 762))

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Abstract

We survey the current status of the time-space complexity of various basic computational problems. For time-space (or space alone) lower bounds, Boolean branching programs are the “ultimate model”. We consider restricted and unrestricted branching program models as well as certain “structured models” which are appropriate to the particular problems being studied. Recent results on graph connectivity are especially noteworthy.

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References

  1. K. Abrahamson: Time-space tradeoffs for algebraic problems on general sequential machines. JCSS 43, 269–289 (1991)

    Google Scholar 

  2. K. Abrahamson: A time-space tradeoff for Boolean Matrix multiplication, In Proc. 31st FOCS, 412–419 (1990)

    Google Scholar 

  3. M. Ajtai, L. Babai, P. Hajnal, J. Komlos, P. Pudlak, V. Rodl, E. Szemeredi, Gy. Turan: Two lower bounds for branching programs, In Proc. 18th ACM STOC, 30–38, (1986)

    Google Scholar 

  4. R. Aleliunas, R.M. Karp, R.J. Lipton, L. Lovasz, C. Rackoff: Random walks, universal traversal sequences, and the complexity of maze problems. In Proc. 20th Annual Symposium on Foundations of Computer Science, 1979, 218–223

    Google Scholar 

  5. N. Alon, W. Maass: Meanders and their applications in lower bounds arguments. JCSS 37, 118–129 (1988)

    Google Scholar 

  6. L. Babai, P. Hajnal, E. Szemeredi, G. Turan: A lower bound for read-once branching program. JCSS 35, 153–162 (1987)

    Google Scholar 

  7. L. Babai, N. Nisan, M. Szegedy: Multiparty protocols, pseudorandom generators for logspace and time-space trade-offs. JCSS 45, 204–232 (1992)

    Google Scholar 

  8. L. Babai, P. Pudlák, V. Rödl, E. Szemerédi, E. Lower bounds to the complexity of symmetric Boolean functions Theoretical Computer Science, vol 74, 313–324 (1990)

    Article  Google Scholar 

  9. A. Bar-Noy, A. Borodin, M. Karchmer, N. Linial, M. Werman: Bounds on universal sequences. SIAM Journal on Computing 18, 268–277 (1989)

    Article  Google Scholar 

  10. G. Barnes, J.F. Buss, W.L. Ruzzo, B. Schieber: A sublinear space, polynomial time algorithm for directed s-t connectivity. In Proc. 7th Annual Conference on Structure in Complexity Theory, 1992, 27–33

    Google Scholar 

  11. G. Barnes, J. Edmonds: Time-space trade-off lower bounds for directed ST-connectivity on JAGs and stronger models. To appear in Proc. 34th Annual Symposium on Foundations of Computer science, 1993

    Google Scholar 

  12. G. Barnes, U. Feige: Short random walks, In ACM STOC93, 728–737 (1993)

    Google Scholar 

  13. G. Barnes, W.L. Ruzzo: Deterministic algorithms for undirected s-t connectivity using polynomial time and sublinear space. In Proc. 23rd Annual ACM Symposium on the Theory of Computing, 1991, 43–45

    Google Scholar 

  14. D.A. Barrington: Bounded-width polynomial-size branching programs recognize exactly those languages in NC1, In Proc. 18th ACM STOC, 1986, 1–5

    Google Scholar 

  15. P. Beame: A general time-space tradeoff for finding unique elments. SIAM Journal on Computing 20, 270–277 (1991)

    Article  Google Scholar 

  16. P. Beame, A. Borodin, P. Raghavan, W.L. Ruzzo, M. Tompa: Time-space tradeoffs for undirected graph connectivity. In Proc. 31st Annual Symposium on Foundations of Computer Science, 1990, 429–438

    Google Scholar 

  17. P. Beame, S. Cook: unpublished manusrcipt

    Google Scholar 

  18. M. Ben-Or, R. Cleve: Computing Algebraic Formulas Using a Constant Number of Registers, In SIAM Journal on Computing 21, 54–58, (1992)

    Article  Google Scholar 

  19. A. Borodin, S. Cook: A time-space tradeoff for sorting on a general sequential model of computation. SIAM Journal on Computing 11, 287–297 (1982)

    Article  Google Scholar 

  20. A. Borodin. D. Dolev, F. Fich, W. Paul: Bounds for width two branching programs. SIAM Journal on Computing 15, 549–560 (1986)

    Article  Google Scholar 

  21. A. Borodin. F. Fich, F. Meyer auf der Heide, E. Upfal, A. Wigderson: A time-space tradeoff for element distinctness. SIAM Journal on Computing 16, 97–99 (1987)

    Article  Google Scholar 

  22. A. Borodin, M.J. Fischer, D.G. Kirkpatrick, N.A. Lynch, M. Tompa: A time-space tradeoff for sorting on non-oblivious machines. JCSS 22, 351–364 (1979)

    Google Scholar 

  23. A. Borodin, A. Razborov, R. Smolensky: On lower bounds for read-k times branching programs. Computational Complexity 3, 1–18 (1993)

    Article  Google Scholar 

  24. A. Borodin, W.L. Ruzzo, M. Tompa: Lower bounds on the length of universal traversal sequences. JCSS 45, 180–203 (1992)

    Google Scholar 

  25. A.Z. Broder, A.R. Karlin, P. Raghavan, E. Upfal: Trading space for time in undirected s-t connectivity. In Proc. 21st Annual ACM Symposium on the Theory of Computing, 1989, 543–549

    Google Scholar 

  26. A.R. Bruss, A.R. Meyer: On time-space classes and their relation to the theory of real addition. Theoretical Computer Science 11, 59–69 (1980)

    Article  Google Scholar 

  27. A. Chandra, M. Furst, R. Lipton: Multiparty protocols, In Proc. 15th ACM STOC, 94–99 (1983)

    Google Scholar 

  28. R. Cleve: Towards Optimal Simulations of Formulas by Bounded-Width Programs, Computational Complexity 1, 91–105, (1991)

    Article  Google Scholar 

  29. A. Cobham: The Recognition problem for the set of perfect squares. IBM Watson Research Center, Research paper RC-1704 (1966)

    Google Scholar 

  30. S.A. Cook, C.W. Rackoff: Space lower bounds for maze threadability on restricted machines. SIAM Journal on Computing 9, 636–652 (1980)

    Article  Google Scholar 

  31. P. Duris, Z. Galil: A time-space tradeoff for language recognition. In Proc. 22nd Annual Symposium on Foundations of Computer Science, 1981, 53–57

    Google Scholar 

  32. J. Edmonds: Time-space lower bounds for undirected and directed ST-connectivity on JAG models. Ph.D. thesis, University of Toronto, 1993

    Google Scholar 

  33. J. Edmonds: Time-space trade-offs for undirected st-connectivity on a JAG. In Proc. 25th Annual ACM Symposium on the Theory of Computing, 1993, 718–727

    Google Scholar 

  34. U. Feige: A randomized time-space tradoff of 0(mR) for USTCON: To appear in FOCS 93

    Google Scholar 

  35. D. Grigoriev: An Application of separability and independence notions for proving lower bounds of circuit complexity. Notes of Scientific Seminars, 60, Leningrad Department, Steklov Mathematical Institute, 1976, 38–48 (in Russian)

    Google Scholar 

  36. J.E. Hopcroft, W.J. Paul, L.G. Valiant: On time versus space and related problems, JACM vol 24, number 2, 332–337 (1977)

    Article  Google Scholar 

  37. N. Immerman: Nonderterministic space is closed under complementation. SIAM Journal on Computing 17, 935–938 (1988)

    Article  Google Scholar 

  38. J.D. Kahn, N. Linial, N. Nisan, M.E. Saks: On the cover time of random walks on graphs. Journal of Theoretical Probability 2, 121–128 (1989)

    Article  Google Scholar 

  39. M. Karchmer: Two time-space tradeoffs for element distinctness. Theoretical Computer Science 47, 237–246 (1986)

    Article  Google Scholar 

  40. S.R. Kosaraju: Parallel Evaluation of Division-Free Arithmetic Expressions, Proc. of 18th Annual ACM Symp. on Theory of Computing, 1986, pp. 231–239.

    Google Scholar 

  41. C.Y. Lee: Representation of switching circuits by binary-decision programs. Bell System Technical Journal 38, 985–999 (1959)

    Google Scholar 

  42. T. Lengauer, R.E. Tarjan: Asymptotically tight bounds on time-space trade-offs in a pebble game. JACM 29, 1087–1130 (1982)

    Article  Google Scholar 

  43. Y. Mansour, N. Nisan, P. Tiwari: The computational complexity of universal hashing. In Proc. 22nd Annual ACM Symposium on the Theory of Computing, 1990, 235–243

    Google Scholar 

  44. W. Masek: A fast algorithm for the string editing problem and decision graph complexity. M.Sc. thesis, Massachusetts Institute of Technology, Cambridge, 1976

    Google Scholar 

  45. N. Nisan: \(RL \subseteq SC\), In Proc. 24th Annual ACM Symposium on the Theory of Computing, 1992, 619–623

    Google Scholar 

  46. E.A. Okolnishnikova: Lower bounds for branching programs computing characteristic functions of binary codes. Metody Discretnogo Analiza 51, 61–83 (1991) (in Russian)

    Google Scholar 

  47. B. Patt-Shamir, D. Pelag: Time-space tradeoffs for Set Operations, Theoretical Computer Science 110, 99–129 (1993)

    Article  Google Scholar 

  48. W.J. Paul, R.E. Tarjan: Time-space trade-offs in a pebble game. Acta Informatica 10, 111–115 (1978)

    Article  Google Scholar 

  49. W.J. Paul, R.E. Tarjan, J.R. Celoni Space Bounds for a Game on Graphs, Mathematical Systems Theory, vol 10, number 3, 239–251 (1977) (See also Correction in vol 11,number 1,page 85, 1977)

    Article  Google Scholar 

  50. N. Pippenger: Pebbling. In Proc. 5th IBM Symposium on Mathematical Foundations of Computer Science, 1980

    Google Scholar 

  51. N. Pippenger: A time-space trade-off, J. ACM 25, 509–515 (1978)

    Article  Google Scholar 

  52. C.K. Poon: Space bounds for graph connectivity problems on node-named JAGs and node-ordered JAGs. To appear in Proc. 34th Annual Symposium on Foundations of Computer science, 1993

    Google Scholar 

  53. A. Razborov: Lower bounds for deterministic and nondeterministic branching programs. In Proc. 8th FCT, Lecture Notes in Computer Scienc, 529, New York/Berlin, 1991, Springer-Verlag, 47–60

    Google Scholar 

  54. R. Reischuk: Improved bounds on the problem of time-space trade-off in the pebble game, J. ACM 27, 839–850 (1980)

    Article  Google Scholar 

  55. J.E. Savage: Space-time tradeoffs — A survey. In Proc. 3rd Hungarian Computer Science Conference, 1981

    Google Scholar 

  56. J.E. Savage, S. Swamy: Space-time tradeoffs on the FFT algorithm. IEEE Trans. Inform. Theory 24, 563–568 (1978)

    Article  Google Scholar 

  57. W.J. Savitch: Relationships between nondeterministic and deterministic tape complexities. JCSS 4, 177–192 (1970)

    Google Scholar 

  58. J. Shearer: unpublished manuscript

    Google Scholar 

  59. R. Szelepcsényi: The method of forcing for nondeterministic automata. Bullaėuropean Assoc. Theoret. Comput. Sci. 33, 96–100 (1987)

    Google Scholar 

  60. M. Tompa: Time-space tradeoffs for computing functions, using connectivity properties of their circuits. JCSS 20, 118–132 (1980)

    Google Scholar 

  61. M. Tompa: Two Familiar Transitive Closure Algorithms which Admit no Polynomial Time, Sublinear Space Implementations, Siam Journal on Computing vol 11, no. 1, 130–137 (1982)

    Article  Google Scholar 

  62. A.C. Yao: Near-optimal time-space tradeoff for element distinctness. In Proc. 29th Annual Symposium on Foundations of Computer Science, 1988, 91–97. Accepted for publication in Siam Journal on Computing.

    Google Scholar 

  63. Y. Yesha: Time-space tradeoffs for matrix multiplication and the discrete Fourier transform on any general sequential random-access computer. SIAM Journal on Computing 29, 183–197 (1984)

    Google Scholar 

  64. S. Zak: An exponential lower bound for one-time-only branching programs. In Proc. 11th MFCT, Lecture Notes in Computer Science, 176, New York/Berlin, 1984, Springer-Verlag, 562–566

    Google Scholar 

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K. W. Ng P. Raghavan N. V. Balasubramanian F. Y. L. Chin

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© 1993 Springer-Verlag Berlin Heidelberg

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Borodin, A. (1993). Time space tradeoffs (getting closer to the barrier?). In: Ng, K.W., Raghavan, P., Balasubramanian, N.V., Chin, F.Y.L. (eds) Algorithms and Computation. ISAAC 1993. Lecture Notes in Computer Science, vol 762. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-57568-5_251

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  • DOI: https://doi.org/10.1007/3-540-57568-5_251

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