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New Bounds for the Garden-Hose Model

Authors Hartmut Klauck, Supartha Podder

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Hartmut Klauck
Supartha Podder

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Hartmut Klauck and Supartha Podder. New Bounds for the Garden-Hose Model. In 34th International Conference on Foundation of Software Technology and Theoretical Computer Science (FSTTCS 2014). Leibniz International Proceedings in Informatics (LIPIcs), Volume 29, pp. 481-492, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2014) https://doi.org/10.4230/LIPIcs.FSTTCS.2014.481

Abstract

We show new results about the garden-hose model. Our main results include improved lower bounds based on non-deterministic communication complexity (leading to the previously unknown Theta(n) bounds for Inner Product mod 2 and Disjointness), as well as an O(n * log^3(n) upper bound for the Distributed Majority function (previously conjectured to have quadratic complexity). We show an efficient simulation of formulae made of AND, OR, XOR gates in the garden-hose model, which implies that lower bounds on the garden-hose complexity GH(f) of the order Omega(n^{2+epsilon}) will be hard to obtain for explicit functions. Furthermore we study a time-bounded variant of the model, in which even modest savings in time can lead to exponential lower bounds on the size of garden-hose protocols.

Subject Classification

Keywords
  • Space Complexity
  • Communication Complexity
  • Garden-Hose Model

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References

  1. D. A. Barrington. Width-3 permutation branching programs, 1985. Technical report, MIT/LCS/TM-293. Google Scholar
  2. P. Beame, M. Tompa, and P. Yan. Communication-space tradeoffs for unrestricted protocols. SIAM Journal on Computing, 23(3):652-661, 1994. Earlier version in FOCS'90. Google Scholar
  3. Joshua Brody, Shiteng Chen, Periklis A. Papakonstantinou, Hao Song, and Xiaoming Sun. Space-bounded communication complexity. In Proceedings of the 4th conference on Innovations in Theoretical Computer Science, pages 159-172, 2013. Google Scholar
  4. Harry Buhrman, Serge Fehr, Christian Schaffner, and Florian Speelman. The garden-hose model. In Proceedings of the 4th conference on Innovations in Theoretical Computer Science, pages 145-158. ACM, 2013. Google Scholar
  5. Well Y. Chiu, Mario Szegedy, Chengu Wang, and Yixin Xu. The garden hose complexity for the equality function. arXiv:1312.7222, 2013. Google Scholar
  6. O. Giel. Branching program size is almost linear in formula size. Journal of Computer and System Sciences, 63(2):222-235, 2001. Google Scholar
  7. H. Klauck. Quantum and classical communication-space tradeoffs from rectangle bounds. In Proceedings of FSTTCS, 2004. Google Scholar
  8. H. Klauck. One-Way Communication Complexity and the Nečiporuk Lower Bound on Formula Size. SIAM J. Comput., 37(2):552-583, 2007. Google Scholar
  9. H. Klauck, R. Špalek, and R. de Wolf. Quantum and classical strong direct product theorems and optimal time-space tradeoffs. SIAM Journal on Computing, 36(5):1472-1493, 2007. Earlier version in FOCS'04. quant-ph/0402123. Google Scholar
  10. Eyal Kushilevitz and Noam Nisan. Communication Complexity. Cambridge University Press, 1997. Google Scholar
  11. K. J. Lange, P. McKenzie, and A. Tapp. Reversible space equals deterministic space. Journal of Computer and System Sciences, 2(60):354-367, 2000. Google Scholar
  12. E. I. Nečiporuk. A boolean function. Soviet Mathematics Doklady, 7(S 999), 1966. Google Scholar
  13. I. Newman. Private vs. common random bits in communication complexity. Information Processing Letters, 39(2):67-71, 1991. Google Scholar
  14. Ilan Newman and Mario Szegedy. Public vs. private coin flips in one round communication games (extended abstract). In Proceedings of the Twenty-eighth Annual ACM Symposium on Theory of Computing, STOC'96, pages 561-570, 1996. Google Scholar
  15. Noam Nisan and Avi Wigderson. Rounds in communication complexity revisited. SIAM J. Comput., 22(1):211-219, February 1993. Google Scholar
  16. C. H. Papadimitriou and M. Sipser. Communication complexity. Journal of Computer and System Sciences, 28(2):260-269, 1984. Earlier version in STOC'82. Google Scholar
  17. P. Papakonstantinou, D. Scheder, and H. Song. Overlays and limited memory communication mode(l)s. In Proc. of the 29th Conference on Computational Complexity, 2014. Google Scholar
  18. I. S. Sergeev. Upper bounds for the formula size of symmetric boolean functions. Russian Mathematics, Iz. VUZ, 58(5):30-42, 2014. Google Scholar
  19. Rakesh Kumar Sinha and Jayram S Thathachar. Efficient oblivious branching programs for threshold and mod functions. Journal of Computer and System Sciences, 55(3):373-384, 1997. Google Scholar
  20. I. Wegener. The Complexity of Boolean Functions. Wiley-Teubner Series in Computer Science, 1987. Google Scholar
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