Amortized Communication Complexity of an Equality Predicate

  • Vladimir Nikishkin
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7913)

Abstract

We study the communication complexity of the direct sum of independent copies of the equality predicate. We prove that the probabilistic communication complexity of this problem is equal to O(N); the computational complexity of the proposed protocol is polynomial in the size of inputs. Our protocol improves the result achieved in 1991 by Feder et al. Our construction is based on two techniques: Nisan’s pseudorandom generator (1992, Nisan) and Smith’s string synchronization algorithm (2007, Smith).

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Kushilevitz, E., Nisan, N.: Communication Complexity. Cambridge Univ. Press (1997)Google Scholar
  2. 2.
    Chuklin, A.: Effective protocols for low-distance file synchronization. arXiv:1102.4712 (2011)Google Scholar
  3. 3.
    Orlitsky, A.: Interactive communication of balanced distributions and of correlated files. SIAM Journal on Discrete Mathematics 6, 548–564 (1993)MathSciNetMATHCrossRefGoogle Scholar
  4. 4.
    Nisan, N.: Pseudorandom Generators for Spacebounded Computation. Combinatorica 12(4), 449–461 (1992)MathSciNetMATHCrossRefGoogle Scholar
  5. 5.
    Nisan, N., Widgerson, N.: Hardness vs. Randomness. Journal of Computer and System Sciences 49(2), 149–167 (1994)MathSciNetMATHCrossRefGoogle Scholar
  6. 6.
    Canetti, R., Goldreich, O.: Bounds on Tradeoffs between Randomness and Communication Complexity. Computational Complexity 3(2), 141–167 (1990)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Newman, L.: Private vs. Common Random Bits in Communication Complexity. Information Processing Letters 39(2), 67–71 (1991)MathSciNetMATHCrossRefGoogle Scholar
  8. 8.
    Impagliazzo, R., Nisan, N., Widgerson, A.: Pseudorandomness for Network Algorithms. In: Proc. of the 26th ACM Symposium on Theory of Computing, pp. 356–364 (1994)Google Scholar
  9. 9.
    Smith, A.: Scrambling Adversarial Errors Using Few Random Bits, Optimal Information Reconciliation, and Better Private Codes. In: Proc. of the 18th ACM-SIAM Symposium on Discrete Algorithms, pp. 395–404 (2007)Google Scholar
  10. 10.
    Nisan, N., Zukerman, D.: Randomness is Linear in Space. 1993 Journal of Computer and System Sciences 52(1), 43–52 (1996)MATHCrossRefGoogle Scholar
  11. 11.
    Feder, T., Kushilevitz, E., Naor, M., Nisan, N.: Amortized Communication Complexity. SIAM J. Comput. 24(4), 736–750 (1991)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Bose, R.C.M., Ray-Chaudhuri, D.K.: On A Class of Error Correcting Binary Group Codes. Information and Control 3(1), 68–79 (1960)MathSciNetMATHCrossRefGoogle Scholar
  13. 13.
    Berlekamp, E.R.: Nonbinary BCH decoding. IEEE Transactions on in Information Theory 14(2), 242 (1967)CrossRefGoogle Scholar
  14. 14.
    Karchmer, M., Raz, R., Wigderson, A.: On Proving Super-Logarithmic Depth Lower Bounds via the Direct Sum in Communication Complexity. In: Proc. of 6th IEEE Structure in Complexity Theory, pp. 299–304 (1991)Google Scholar
  15. 15.
    Parnafes, I., Raz, R., Wigderson, A.: Direct Product Results and the GCD Problem, in Old and New Communication Models. In: STOC 1997 Proceedings of the Twenty-ninth Annual ACM Symposium on Theory of Computing, pp. 363–372 (1997)Google Scholar
  16. 16.
    Chakrabarti, A., Shi, Y., Wirth, A., Yao, A.: Informational Complexity and the Direct Sum Problem for Simultaneous Message Complexity. In: Proceedings of 42nd IEEE Symposium on Foundations of Computer Science (2001)Google Scholar
  17. 17.
    Sherstov, A.: Strong Direct Produce Theorems for Quantum Communication and Query Complexity. In: STOC 2011 Proceedings of the 43rd Annual ACM Symposium on Theory of Computing, pp. 41–50 (2011)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Vladimir Nikishkin
    • 1
  1. 1.Moscow Institute of Physics and TechnologyRussia

Personalised recommendations