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Annual Symposium on Theoretical Aspects of Computer Science

STACS 2001: STACS 2001 pp 206–217Cite as

On Multipartition Communication Complexity

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2010))

Abstract

We study k-partition communication protocols, an extension of the standard two-party best-partition model to k input partitions. The main results are as follows.

  1. 1.

    A strong explicit hierarchy on the degree of non-obliviousness is established by proving that, using k+1 partitions instead of k may decrease the commu- nication complexity from θ (n) to θ (log k).

  2. 2.

    Certain linear codes are hard for k-partition protocols even when k may be exponentially large (in the input size). On the other hand, one can show that all characteristic functions of linear codes are easy for randomized OBDDs.

  3. 3.

    It is proven that there are subfunctions of the triangle-freeness function and the function ⊕ CLIQUEn,3 which are hard for multipartition protocols. As an application, truly exponential lower bounds on the size of nondeterministic read-once branching programs for these functions are obtained, solving an open problem of Razborov [17].

The work of the first and second author has been supported by DFG grant Hr 14/3-2, and of the fourth author by DFG grant We 1066/9-1.

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References

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

    Google Scholar 

  2. M. Ajtai, L. Babai, P. Hajnal, J. Komlos, P. Pudlák, V. Rödl, E. Szemeredi, and Gy. Turán, Two lower bounds for branching programs, in: Proc. 18th ACM STOC, 1986, pp. 30–38.

    Google Scholar 

  3. P. Beame, M. Saks, X. Sun, and E. Vee, Super-linear time-space tradeoff lower bounds for randomized computation, Technical Report 25, Electr. Coll. on Comp. Compl., 2000.

    Google Scholar 

  4. P. Beame, M. Saks, and J. S. Thathachar, Time-space tradeoffs for branching programs, in: Proc. of 39th FOCS, 1998, pp. 254–263.

    Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  6. A. Hajnal, W. Maass, and G. Turán, On the communication complexity of graph properties, in: Proc. of 20th ACM STOC, 1988, pp. 186–191.

    Google Scholar 

  7. J. Hromkovič, Communication Complexity and Parallel Computing, EATCS Texts in Theoretical Computer Science, Springer-Verlag, 1997.

    Google Scholar 

  8. J. Hromkovič and M. Sauerhoff, Tradeoffs between nondeterminism and complexity for communication protocols and branching programs, in: Proc. of STACS 2000, LNCS 1770, pp. 145–156.

    Chapter  Google Scholar 

  9. S. Jukna, A note on read-k-times branching programs, RAIRO Theor. Inf. and Applications 29:1 (1995), pp. 75–83.

    MATH  MathSciNet  Google Scholar 

  10. S. Jukna and A. Razborov, Neither reading few bits twice nor reading illegally helps much, Discrete Appl. Math. 85:3 (1998), pp. 223–238.

    Article  MATH  MathSciNet  Google Scholar 

  11. S. Jukna and G. Schnitger, On the complexity of graphs which lack small cliques, manuscript.

    Google Scholar 

  12. E. Kushilevitz and N. Nisan, Communication Complexity, Cambridge University Press, 1997.

    Google Scholar 

  13. F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, North-Holland, 1998.

    Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  15. E. A. Okol’nishnikova, On Lower Bounds for Branching Programs, Siberian Advances in Mathematics 3:1 (1998), pp. 152–166.

    MathSciNet  Google Scholar 

  16. Ch. H. Papadimitriou and M. Sipser, Communication complexity, J. Comput. Syst. Sci. 28 (1984), pp. 260–269.

    Article  MATH  MathSciNet  Google Scholar 

  17. A. Razborov, Lower bounds for deterministic and nondeterministic branching programs, in: Proc. of FCT’ 91, Lecture Notes in Computer Science 529, Springer-Verlag 1991, pp. 47–60.

    Google Scholar 

  18. A. Yao, The entropic limitations of VLSI computations, in: Proc. 13th ACM STOC (1981), pp. 308–311.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Lehrstuhl für Informatik I RWTH Aachen, Ahornstraße 55, 52074, Aachen, Germany

    Pavol Ďuriš & Juraj Hromkovič

  2. Department of Informatics, Comenius University Mlynska dolina, 84215, Bratislava, Slovakia

    Pavol Ďuriš

  3. Fachbereich Informatik, Johann Wolfgang Goethe-Universität Frankfurt, Robert-Mayer-Straße 11-15, 60054, Frankfurt am Main, Germany

    Stasys Jukna & Georg Schnitger

  4. FB Informatik, LS 2, Universität Dortmund, 44221, Dortmund, Germany

    Martin Sauerhoff

Authors
  1. Pavol Ďuriš
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  2. Juraj Hromkovič
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  3. Stasys Jukna
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  4. Martin Sauerhoff
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  5. Georg Schnitger
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Editor information

Editors and Affiliations

  1. I3S & INRIA Sophia Antipolis INRIA, CNRS, 2004 Route des Lucioles, 06902, Sophia-Antipolis, France

    Afonso Ferreira

  2. Institut für Theoretische Informatik, Fakultät Informatik, TU Dresden, 01062, Dresden, Germany

    Horst Reichel

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© 2001 Springer-Verlag Berlin Heidelberg

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Ďuriš, P., Hromkovič, J., Jukna, S., Sauerhoff, M., Schnitger, G. (2001). On Multipartition Communication Complexity. In: Ferreira, A., Reichel, H. (eds) STACS 2001. STACS 2001. Lecture Notes in Computer Science, vol 2010. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44693-1_18

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  • DOI: https://doi.org/10.1007/3-540-44693-1_18

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-41695-1

  • Online ISBN: 978-3-540-44693-4

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