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Partition Arguments in Multiparty Communication Complexity

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Automata, Languages and Programming (ICALP 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5555))

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Abstract

Consider the “Number in Hand” multiparty communication complexity model, where k players P 1,...,P k holding inputs \(x_1,\ldots,x_k\in{0, 1}^n\) (respectively) communicate in order to compute the value f(x 1,...,x k ). The main lower bound technique for the communication complexity of such problems is that of partition arguments: partition the k players into two disjoint sets of players and find a lower bound for the induced two-party communication complexity problem. In this paper, we study the power of the partition arguments method. Our two main results are very different in nature:

(i) For randomized communication complexity we show that partition arguments may be exponentially far from the true communication complexity. Specifically, we prove that there exists a 3-argument function f whose communication complexity is Ω(n) but partition arguments can only yield an Ω(log n) lower bound. The same holds for nondeterministic communication complexity.

(ii) For deterministic communication complexity, we prove that finding significant gaps, between the true communication complexity and the best lower bound that can be obtained via partition arguments, would imply progress on (a generalized version of) the “log rank conjecture” of communication complexity.

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References

  1. Ajtai, M., Jayram, T.S., Kumar, R., Sivakumar, D.: Approximate counting of inversions in a data stream. In: STOC, pp. 370–379 (2002)

    Google Scholar 

  2. Alon, N., Matias, Y., Szegedy, M.: The space complexity of approximating the frequency moments. J. Comput. Syst. Sci. 58(1), 137–147 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  3. Babai, L., Nisan, N., Szegedy, M.: Multiparty protocols and logspace-hard pseudorandom sequences. In: Proc. of the 21st ACM Symp. on the Theory of Computing, pp. 1–11 (1989)

    Google Scholar 

  4. Bar-Yossef, Z., Jayram, T.S., Kumar, R., Sivakumar, D.: An information statistics approach to data stream and communication complexity. J. Comput. Syst. Sci. 68(4), 702–732 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  5. Chakrabarti, A., Khot, S., Sun, X.: Near-optimal lower bounds on the multi-party communication complexity of set disjointness. In: IEEE Conference on Computational Complexity, pp. 107–117 (2003)

    Google Scholar 

  6. Chandra, A., Furst, M., Lipton, R.: Multiparty protocols. In: Proc. of the 15th ACM Symp. on the Theory of Computing, pp. 94–99 (1983)

    Google Scholar 

  7. Dietzfelbinger, M., Hromkovic, J., Schnitger, G.: A comparison of two lower-bound methods for communication complexity. Theor. Comput. Sci. 168(1), 39–51 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  8. Dolev, D., Feder, T.: Multiparty communication complexity. In: Proc. of the 30th IEEE Symp. on Foundations of Computer Science, pp. 428–433 (1989)

    Google Scholar 

  9. Dolev, D., Feder, T.: Determinism vs. nondeterminism in multiparty communication complexity. SIAM J. Comput. 21(5), 889–895 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  10. Duris, P.: Multiparty communication complexity and very hard functions. Inf. Comput. 192(1), 1–14 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  11. Duris, P., Rolim, J.D.P.: Lower bounds on the multiparty communication complexity. J. Comput. Syst. Sci. 56(1), 90–95 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  12. Feder, T., Kushilevitz, E., Naor, M., Nisan, N.: Amortized communication complexity. SIAM J. Comput. 24(4), 736–750 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  13. Gronemeier, A.: Asymptotically optimal lower bounds on the nih-multi-party information complexity of the and-function and disjointness. In: STACS 2009, pp. 505–516 (2009)

    Google Scholar 

  14. Håstad, J.: Tensor rank is NP-complete. J. Algorithms 11(4), 644–654 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  15. Karchmer, M., Wigderson, A.: Monotone circuits for connectivity require super-logarithmic depth. In: Proc. of the 20th ACM Symp. on the Theory of Computing, pp. 539–550 (1988)

    Google Scholar 

  16. Kushilevitz, E., Nisan, N.: Communication Complexity. Cambridge University Press, Cambridge (1997)

    Book  MATH  Google Scholar 

  17. Lipton, R.J., Sedgewick, R.: Lower bounds for VLSI. In: Proc. of the 13rd ACM Symp. on the Theory of Computing, pp. 300–307 (1981)

    Google Scholar 

  18. Mehlhorn, K., Schmidt, E.M.: Las vegas is better than determinism in VLSI and distributed computing. In: Proc. of the 14th ACM Symp. on the Theory of Computing, pp. 330–337 (1982)

    Google Scholar 

  19. Newman, I.: Private vs. common random bits in communication complexity. Inf. Process. Lett. 39(2), 67–71 (1991)

    Article  MathSciNet  MATH  Google Scholar 

  20. Nisan, N., Wigderson, A.: On rank vs. communication complexity. Combinatorica 15(4), 557–565 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  21. Raz, R., Spieker, B.: On the “log rank”-conjecture in communication complexity. Combinatorica 15(4), 567–588 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  22. van Lint, J.H., Wilson, R.M.: A Course in Combinatorics. Cambridge University Press, Cambridge (1992)

    MATH  Google Scholar 

  23. Yao, A.C.: Some complexity questions related to distributed computing. In: Proc. of the 11th ACM Symp. on the Theory of Computing, pp. 209–213 (1979)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Mathematics and Computer Science, Technische Universiteit Eindhoven, and CWI Amsterdam, Netherlands

    Jan Draisma

  2. Computer Science Department, Technion Israel Institute of Technology, Haifa, Italy

    Eyal Kushilevitz & Enav Weinreb

Authors
  1. Jan Draisma
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  2. Eyal Kushilevitz
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  3. Enav Weinreb
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Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Freiburg, Georges Köhler Allee 79, 79110, Freiburg, Germany

    Susanne Albers

  2. Department of Computer and Systems Sciences, Sapienza University of Rome, Via Ariosto 25, 00184, Roma, Italy

    Alberto Marchetti-Spaccamela

  3. Google R&D Center, School of Computer Science, Tel Aviv University, 69978, Tel Aviv, Israel

    Yossi Matias

  4. University of Patras and CTI, N. Kazantzaki Street 1, 26504 Rion, Patras, Greece

    Sotiris Nikoletseas

  5. RWTH Aachen, Lehrstuhl Informatik 7, Ahornstraße 55, 52056, Aachen, Germany

    Wolfgang Thomas

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© 2009 Springer-Verlag Berlin Heidelberg

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Draisma, J., Kushilevitz, E., Weinreb, E. (2009). Partition Arguments in Multiparty Communication Complexity. In: Albers, S., Marchetti-Spaccamela, A., Matias, Y., Nikoletseas, S., Thomas, W. (eds) Automata, Languages and Programming. ICALP 2009. Lecture Notes in Computer Science, vol 5555. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02927-1_33

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  • DOI: https://doi.org/10.1007/978-3-642-02927-1_33

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-02926-4

  • Online ISBN: 978-3-642-02927-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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