Space-time tradeoffs for oblivious integer multiplication

  • John E. Savage
  • Sowmitri Swamy
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 71)


An extension of a result by Grigoryev is used to derive a lower bound on the space-time product required for integer multiplication when realized by straight-line algorithms. If S is the number of temporary storage locations used by a straight-line algorithm on a random-access machine and T is the number of computation steps, then we show that (S+1)T ⩾ Ω(n2) for binary integer multiplication when the basis for the straight-line algorithm is a set of Boolean functions.


Boolean Function Integer Multiplication Combinatorial Argument Pebble Game Oblivious Algorithm 
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  1. 1.
    Paterson, M. S. and C. E. Hewitt, "Comparative Schematology," Proj. MAC Conf. on Concurrent Systems and Parallel Computation, Woods Hole, Massachusetts, pp. 119–127, June 2–5, 1970.Google Scholar
  2. 2.
    Hopcroft, J. E., W. J. Paul, and L. G. Valiant, "On Time Versus Space," JACM, Vol. 24, No. 2, pp. 332–337, 1977.Google Scholar
  3. 3.
    Paul, W. J., R. E. Tarjan, and J. R. Celoni, "Space Bounds for a Game on Graphs," Eighth Ann. Symp. on Theory of Computing, Hershey, Pennsylvania, pp. 149–160, May 3–5, 1976.Google Scholar
  4. 4.
    Savage, J. E., "Computational Work and Time on Finite Machines," JACM, Vol. 19, No. 4, pp. 660–674, 1972.Google Scholar
  5. 5.
    Savage, J. E. and S. Swamy, "Space-Time Tradeoffs on the FFT Algorithm," IEEE Transactions on Information Theory, Vol. IT-24, No. 5, pp. 563–568, Sept. 1978.Google Scholar
  6. 6.
    Tompa, M., "Time-Space Tradeoffs for Computing Functions Using Connectivity Properties of their Circuits," Proceedings of the Tenth Annual ACM Symp. on Theory of Computing, pp. 196–204, May 1–3, 1978.Google Scholar
  7. 7.
    Valiant, L. G., "Graph-Theoretic Properties in Computational Complexity," Journal of Computer and System Sciences, Vol. 13, pp. 278–285, 1976.Google Scholar
  8. 8.
    Pippenger, N., "A Time-Space Tradeoff," IBM preprint, May 1977, to appear in JACM.Google Scholar
  9. 9.
    Swamy, S. and J. E. Savage, "Space-Time Tradeoffs for Linear Recursion," Brown University, Computer Science Technical Report No. CS-36, June 1978.Google Scholar
  10. 10.
    Chandra, A. K., "Efficient Compilation of Linear Recursive Programs," IBM Research Report RC4517, 10 pp., August 29, 1973, 14th SWAT Conference.Google Scholar
  11. 11.
    Paul, W. J. and R. E. Tarjan, "Time-Space Tradeoffs in a Pebble Game," Stanford University Technical Report STAN-CS-77-619, July 1977, Fourth Colloq. on Auto. Langs. and Progr., Turku, Finland.Google Scholar
  12. 12.
    Grigoryev, D. Yu., "An Application of Separability and Independence Notions for Proving Lower Bounds on Circuit Complexity," Notes of Scientific Seminars, Steklov Math. Inst., Leningrad, Vol. 60, 1976.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1979

Authors and Affiliations

  • John E. Savage
    • 1
  • Sowmitri Swamy
    • 1
  1. 1.Department of Computer ScienceBrown UniversityProvidenceUSA

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