Skip to main content

Randomized Communication Protocols

(A Survey)

  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2264))

Abstract

There are very few computing models for which the power of randomized computing is as well understood as for communication protocols and their communication complexity. Since the communication complexity is strongly related to several complexity measures of distinct basic models of computation, there exist possibilities to transform some results about randomized communication protocols to other computing models, and so communication complexity has established itself as a powerful instrument for the study of randomization in complexity theory. The aim of this work is to survey the fundamental results about randomized communication complexity with the focus on the comparison of the efficiency of deterministic, nondeterministic and randomized communication.

Supported by the DFG Project Hr.

This is a preview of subscription content, log in via an institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Yao, A.C.: Some complexity questions related to distributive computing. Proc. 11th ACM STOC, ACM 1979, pp. 209–213.

    Google Scholar 

  2. Abelson, H.: Lower bounds on information transfer in distributed computations. Proc. 19th IEEE FOCS, IEEE 1978, pp. 151–158.

    Google Scholar 

  3. Hromkovič, J.: Communication Complexity and Parallel Computing. Springer-Verlag 1997.

    Google Scholar 

  4. Kushilevitz, E., Nisan, N.: Communication Complexity, Cambridge University Press 1997.

    Google Scholar 

  5. Thompson, C.D.: Area-time complexity for VLSI. Proc. 11th ACM STOC, ACM 1979, pp. 81–88.

    Google Scholar 

  6. Thompson, C.D.: A complexity theory for VLSI. Doctoral dissertation. CMU-CS-80-140, Computer Science Department, Carnagie-Mellon University, Pittsburgh, August 1980, pp. 131.

    Google Scholar 

  7. Savage, J.E.: Area-time tradeoffs for matrix multiplication and related problems in VLSI models. J. of Computer and System Sciences 20(1981), pp. 230–242.

    Article  MathSciNet  Google Scholar 

  8. Leiserson, C.E.: Area efficient graph algorithms (for VLSI). Proc. 21st IEEE FOCS, IEEE 1980, pp. 270–281.

    Google Scholar 

  9. Lovász, L.: Communication Complexity: A Survey. Techn. Report CS-TR-204-89, Princeton University, 1989 (also in: Paths, Flows and VLSI Layout (Korte, Lovász, Promel, and Schrijver, eds.), Springer-Verlag 1990, pp. 235–266).

    Google Scholar 

  10. Hromkovič, J.: Some complexity aspects of VLSI computations. Part 1. A framework for the study of information transfer in VLSI circuits. Computers and Artificial Intelligence 7 (1988), pp. 229–252.

    MATH  MathSciNet  Google Scholar 

  11. Ďuriš, P., Galil, Z.: On the power of multiple reads in chip. Information and Computation 104 (1993), pp. 277–287.

    Article  MATH  MathSciNet  Google Scholar 

  12. Karchmer, M., Wigderson, A.: Monotone circuits for connectivity require superlogarithmic depth. Proc. 20th ACM STOC, ACM 1988, pp. 539–550. (also SIAM J. Discrete Mathematics 3 (1990), 718-727).

    Google Scholar 

  13. Alon, N., Maas, W.: Meanders, Ramsey theory and lower bounds for branching programs. Proc. 27th IEEE FOCS, IEEE 1986, pp. 410–417.

    Google Scholar 

  14. Ajtai, M.: A non-linear time lower bound for Boolean branching programs. Proc. 40th IEEE FOCS, IEEE 1999, pp. 60–70.

    Google Scholar 

  15. Beame, P.W., Saks, M., Thathachar, J.S.: Time-space tradeoffs for branching programs. Proc. 39th IEEE FOCS, IEEE 1998, pp. 254–263.

    Google Scholar 

  16. Hromkovič, J.: Nonlinear lower bounds on the number of processors of circuits with sublinear separators. Information and Computation 95 (1991), pp. 117–128.

    Article  MATH  MathSciNet  Google Scholar 

  17. Turán, G.: Lower bounds for synchronous circuits and planar circuits. Information Processing Letters 130(1989), pp. 37–40.

    Article  Google Scholar 

  18. Newman, I.: Private versus common random bits in communication complexity. Information Processing Letters 39 (1991), pp. 67–71.

    Article  MATH  Google Scholar 

  19. Freivalds, R.: Probabilistic machines can use less running time. Information Processing 1977, IFIP, North Holland 1977, pp. 839–842.

    Google Scholar 

  20. Aho, A.V., Ullman, J.D., Yannakakis, M.: On notions of informations transfer in VLSI circuits. Proc. 15th ACM STOC, ACM 1983, pp. 133–139.

    Google Scholar 

  21. Mehlhorn, K., Schmidt, E.: Las Vegas is better than determinism in VLSI and distributed computing. Proc. 14th Annual ACM Symposium on Theory ofComputing, San Francisco, ACM 1982, pp. 330–337.

    Google Scholar 

  22. Hromkovič, J., Schnitger, G.: On the power of Las Vegas for one-way communication complexity, OBDDs, and finite automata. Information and Computation 169 (2001), pp. 284–296.

    Article  MATH  MathSciNet  Google Scholar 

  23. Ja’Ja, J., Prassanna Kamar, V.K., Simon, J.: Information transfer under different sets of protocols. SIAM J. Computing 13 (1984), pp. 840–849.

    Article  MATH  Google Scholar 

  24. Papadimitriou, Ch., Sipser, M.: Communication complexity. Proc. 14th ACM STOC, San Francisco, ACM 1982, pp. 196–200.

    Google Scholar 

  25. Babai, L., Frankl, P., Simon, J.: Complexity classes in communication complexity theory. Proc. 27th IEEE FOCS, IEEE 1986, pp. 337–347.

    Google Scholar 

  26. Kalyanasundaram, B., Schnitger, G.: The probabilistic communication complexity of set intersection. Proc. 2nd Annual Conference on Structure in Complexity Theory, 1987, pp. 41–47.

    Google Scholar 

  27. Razborov, A.A.: On the distributed complexity of disjointness. Proc. 17th ICALP, Springer-Verlag 1990, pp. 249–253. (also Theoretical Computer Science 106 (1992), 385-390.)

    Google Scholar 

  28. Ablayev, F.M.: Lower bounds for one-way probabilistic communication complexity and their application to space complexity. Theoretical Computer Science 157 (1996), pp. 139–159.

    Article  MATH  MathSciNet  Google Scholar 

  29. Chor, B., Goldreich, O.: Unbiased bits from sources of weak randomness and probabilistic communication complexity. Proc. 26th IEEE FOCS, IEEE 1985, pp. 429–442.

    Google Scholar 

  30. Halstenberg, B., Reischuk, R.: On different modes of communication. Proc. 20th ACM STOC, ACM 1988, pp. 162–172.

    Google Scholar 

  31. King, F.P., Abhasel, G.: Communication complexity of computing the Hamming distance. SIAM J. Computing 15 (1986), pp. 932–946.

    Article  MATH  Google Scholar 

  32. Meinel, Ch., Waack, S.: Lower bounds for the majority communication complexity of various graph accessibility problems. Proc. 20th MFCS’95, Lecture Notes in Computer Science 969, Springer-Verlag. 1995, pp.299–308.

    Google Scholar 

  33. Nisan, N., Wigderson, A.: Bounds in communication complexity revised. 32nd ACM STOC, ACM 1991, pp. 419–429 (also in SIAM J. Computing 22 (1993), pp. 211-219).

    Google Scholar 

  34. Yao, A.C.: Lower bounds by probabilistic arguments. Proc. 25th ACM STOC, ACM 1983, pp. 420–428.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2001 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Hromkovič, J. (2001). Randomized Communication Protocols. In: Steinhöfel, K. (eds) Stochastic Algorithms: Foundations and Applications. SAGA 2001. Lecture Notes in Computer Science, vol 2264. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45322-9_1

Download citation

  • DOI: https://doi.org/10.1007/3-540-45322-9_1

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-43025-4

  • Online ISBN: 978-3-540-45322-2

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics