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Lower bounds for the modular communication complexity of various graph accessibility problems

  • Christoph Meinel
  • Stephan Waack
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 911)

Abstract

We investigate the modular communication complexity of the graph accessibility problem GAP and its modular counting versions MODk-GAP, k≥2. Due to arguments concerning variation ranks and certain projection reductions, we prove that, for any partition of the input variables and for any moduls k and m, GAP and MODk-GAP have MOD m -communication complexity Ω(n), where n denotes the number of nodes of the graphs under consideration.

Topics

Computational Complexity Modular Communication Protocols Variation ranks Projection Reductions GAP, MODk-GAP 

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References

  1. 1.
    A. V. Aho, J. D. Ullman, M. Yannakakis, On notions of information transfer in VLSI circuits, in: Proc. 15th ACM STOC 1983, pp. 133–183.Google Scholar
  2. 2.
    L. Babai, P. Frankl, J. Simon, Complexity classes in communication complexity theory, in: Proc. 27th IEEE FOCS, pp. 337–347, 1986.Google Scholar
  3. 3.
    B. Halstenberg, R. Reischuk, Relations between Communication Complexity Classes, in: Proc. 3rd IEEE Structure in Complexity Theory Conference, pp. 19–28, 1988.Google Scholar
  4. 4.
    C. Damm, M. Krause, Ch. Meinel, St. Waack, Separating counting communication complexity classes, in: Proc. 9th STACS, Lecture Notes in Computer Science 577, Springer Verlag 1992, pp. 281–293.Google Scholar
  5. 5.
    A. Hajnal, W. Maass, G. Turan, On the communication complexity of graph problems, in: Proc. 20th ACM STOC 1988, pp. 186–191.Google Scholar
  6. 6.
    N. Immerman, Languages that capture complexity classes, SIAM J. Comput., 16(4)(1978), pp. 760–778.CrossRefGoogle Scholar
  7. 7.
    M. Krause, St. Waack, Variation ranks of communication matrices and lower bounds for depth two circuits having symmetric gates with unbounded fan-in, in: Proc. 32nd IEEE FOCS 1991, pp. 777–782.Google Scholar
  8. 8.
    Ch. Meinel, p-Projection reducibility and the complexity classes L(nonuniform) and NL(nonuniform), in: Proc. 12th MFCS, 1986, LNCS 233, 527–535.Google Scholar
  9. 9.
    Ch. Meinel, Modified branching programs and their computational power, LNCS 370, Springer-Verlag, 1989.Google Scholar
  10. 10.
    Ch. Meinel, St. Waack, Upper and lower bounds for certain graph-accessibility problems on bounded alternating ω-branching programs, in: Complexity Theory-current research, Eds. K. Ambos-Spies, S. Homer, U. Schöning, Cambridge University Press 1993, 273–290.Google Scholar
  11. 11.
    W. Savitch, Relationship between nondeterministic and deterministic tape complexities, J. Comput. System Sci. 4(1970), pp. 244–253.Google Scholar
  12. 12.
    Skyum, L. V. Valiant, A complexity theory based on Boolean algebra, Proc. 22nd IEEE FOCS, pp. 244–253.Google Scholar
  13. 13.
    A. Yao, The entropic limitations of VLSI computations, Proc. 13th ACM STOC 1981, pp. 308–311.Google Scholar
  14. 14.
    A. Yao, On ACC and Threshold Circuits, Proc. 31th IEEE FOCS 1990, pp. 619–627.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  • Christoph Meinel
    • 1
  • Stephan Waack
    • 2
  1. 1.Theoretische Informatik Fachbereich IVUniversität TrierTrier
  2. 2.Inst. für Num. und Angew. MathematikGeorg-August-Univ. GöttingenGöttingen

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