Skip to main content
SpringerLink
Log in
Book cover

International Conference on Theory and Applications of Models of Computation

TAMC 2017: Theory and Applications of Models of Computation pp 529–542Cite as

Nondeterministic Communication Complexity of Random Boolean Functions (Extended Abstract)

  • Conference paper
  • First Online:

  • 783 Accesses

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10185))

Abstract

We study nondeterministic communication complexity and related concepts (fooling sets, fractional covering number) of random functions \(f:X\times Y \rightarrow \{0,1\}\) where each value is chosen to be 1 independently with probability \(p=p(n)\), \(n := {\left|{X}\right|}={\left|{Y}\right|}\).

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

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 EPUB and 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

References

  1. Alon, N., Spencer, J.H.: The Probabilistic Method. Wiley, New York (2008)

    Book  MATH  Google Scholar 

  2. Beasley, L.B., Klauck, H., Lee, T., Theis, D.O.: Communication complexity, linear optimization, and lower bounds for the nonnegative rank of matrices (dagstuhl seminar 13082). Dagstuhl Rep. 3(2), 127–143 (2013)

    Google Scholar 

  3. Bollobás, B.: Random Graphs. Cambridge Studies in Advanced Mathematics, vol. 73, 2nd edn. Cambridge University Press, Cambridge (2001)

    Book  MATH  Google Scholar 

  4. Braun, G., Fiorini, S., Pokutta, S.: Average case polyhedral complexity of the maximum stable set problem. In: Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques, APPROX/RANDOM 2014, Barcelona, Spain, 4–6 September 2014, pp. 515–530 (2014). http://dx.doi.org/10.4230/LIPIcs.APPROX-RANDOM.2014.515

  5. Dani, V., Moore, C.: Independent sets in random graphs from the weighted second moment method. In: Goldberg, L.A., Jansen, K., Ravi, R., Rolim, J.D.P. (eds.) APPROX/RANDOM 2011. LNCS, vol. 6845, pp. 472–482. Springer, Heidelberg (2011). doi:10.1007/978-3-642-22935-0_40

    Chapter  Google Scholar 

  6. Dawande, M., Keskinocak, P., Swaminathan, J.M., Tayur, S.: On bipartite and multipartite clique problems. J. Algorithms 41(2), 388–403 (2001). http://dx.doi.org/10.1006/jagm.2001.1199

  7. Dawande, M., Keskinocak, P., Tayur, S.: On the biclique problem in bipartite graphs. Carnegie Mellon University (1996). GSIA Working Paper

    Google Scholar 

  8. Dietzfelbinger, M., Hromkovič, J., Schnitger, G.: A comparison of two lower-bound methods for communication complexity. Theoret. Comput. Sci. 168(1), 39–51 (1996). http://dx.doi.org/10.1016/S0304-3975(96)00062-X, 19th International Symposium on Mathematical Foundations of Computer Science, Košice (1994)

  9. Fiorini, S., Kaibel, V., Pashkovich, K., Theis, D.O.: Combinatorial bounds on nonnegative rank and extended formulations. Discrete Math. 313(1), 67–83 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  10. Fiorini, S., Massar, S., Pokutta, S., Tiwary, H.R., Wolf, R.: Linear vs. semidefinite extended formulations: exponential separation and strong lower bounds. In: STOC (2012)

    Google Scholar 

  11. Fiorini, S., Massar, S., Pokutta, S., Tiwary, H.R., Wolf, R.D.: Exponential lower bounds for polytopes in combinatorial optimization. J. ACM (JACM) 62(2), 17 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  12. Froncek, D., Jerebic, J., Klavzar, S., Kovár, P.: Strong isometric dimension, biclique coverings, and sperner’s theorem. Comb. Probab. Comput. 16(2), 271–275 (2007). http://dx.doi.org/10.1017/S0963548306007711

    Article  MathSciNet  MATH  Google Scholar 

  13. Goemans, M.X.: Smallest compact formulation for the permutahedron. Math. Program. 153(1), 5–11 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  14. Hajiabolhassan, H., Moazami, F.: Secure frameproof code through biclique cover. Discrete Math. Theor. Comput. Sci. 14(2), 261–270 (2012). http://www.dmtcs.org/dmtcs-ojs/index.php/dmtcs/article/view/2131/4075

    MathSciNet  MATH  Google Scholar 

  15. Hajiabolhassan, H., Moazami, F.: Some new bounds for cover-free families through biclique covers. Discrete Math. 312(24), 3626–3635 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  16. Izhakian, Z., Janson, S., Rhodes, J.: Superboolean rank and the size of the largest triangular submatrix of a random matrix. Proc. Am. Math. Soc. 143(1), 407–418 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  17. Janson, S., Łuczak, T., Rucinski, A.: Random Graphs. Wiley-Interscience Series in Discrete Mathematics and Optimization. Wiley-Interscience, New York (2000)

    Book  MATH  Google Scholar 

  18. Kaibel, V.: Extended formulations in combinatorial optimization. Optima - Math. Optim. Soc. Newsl. 85, 2–7 (2011). www.mathopt.org/Optima-Issues/optima85.pdf

  19. Karp, R.M., Sipser, M.: Maximum matchings in sparse random graphs. In: FOCS, pp. 364–375 (1981)

    Google Scholar 

  20. Klauck, H., Lee, T., Theis, D.O., Thomas, R.R.: Limitations of convex programming: lower bounds on extended formulations and factorization ranks (dagstuhl seminar 15082). Dagstuhl Rep. 5(2), 109–127 (2015)

    Google Scholar 

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

    Book  MATH  Google Scholar 

  22. Lonardi, S., Szpankowski, W., Yang, Q.: Finding biclusters by random projections. In: Sahinalp, S.C., Muthukrishnan, S., Dogrusoz, U. (eds.) CPM 2004. LNCS, vol. 3109, pp. 102–116. Springer, Heidelberg (2004). doi:10.1007/978-3-540-27801-6_8

    Chapter  Google Scholar 

  23. Lonardi, S., Szpankowski, W., Yang, Q.: Finding biclusters by random projections. Theor. Comput. Sci. 368(3), 217–230 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  24. Lovás, L., Saks, M.: Communication complexity and combinatorial lattice theory. J. Comput. Syst. Sci. 47, 322–349 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  25. Mitzenmacher, M., Upfal, E.: Probability and Computing – Randomized Algorithms and Probabilistic Analysis. Cambridge University Press, Cambridge (2006)

    Google Scholar 

  26. Park, G., Szpankowski, W.: Analysis of biclusters with applications to gene expression data. In: International Conference on Analysis of Algorithms. DMTCS Proc. AD, vol. 267, p. 274 (2005)

    Google Scholar 

  27. Roughgarden, T.: Communication complexity (for algorithm designers). arXiv preprint arXiv:1509.06257 (2015)

  28. Schrijver, A.: Combinatorial Optimization. Polyhedra and Efficiency. Algorithms and Combinatorics, vol. 24. Springer, Berlin (2003)

    Google Scholar 

  29. Sun, X., Nobel, A.B.: On the size and recovery of submatrices of ones in a random binary matrix. J. Mach. Learn. Res 9, 2431–2453 (2008)

    MathSciNet  MATH  Google Scholar 

  30. Yannakakis, M.: Expressing combinatorial optimization problems by linear programs. J. Comput. Syst. Sci. 43(3), 441–466 (1991). http://dx.doi.org/10.1016/0022-0000(91)90024-Y

Download references

Acknowledgments

The authors would like to thank the anonymous referees for their valuable comments.

Dirk Oliver Theis is supported by Estonian Research Council, ETAG (Eesti Teadusagentuur), through PUT Exploratory Grant #620. Mozhgan Pourmoradnasseri is recipient of the Estonian IT Academy Scholarship. This research is supported by the European Regional Fund through the Estonian Center of Excellence in Computer Science, EXCS.

Author information

Authors and Affiliations

  1. Institute of Computer Science, University of Tartu, Ülikooli 17, 51014, Tartu, Estonia

    Mozhgan Pourmoradnasseri & Dirk Oliver Theis

Authors
  1. Mozhgan Pourmoradnasseri
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Dirk Oliver Theis
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Dirk Oliver Theis .

Editor information

Editors and Affiliations

  1. Anna University, Chennai, India

    T.V. Gopal

  2. Universität Bern , Bern, Switzerland

    Gerhard Jäger

  3. Universität Bern , Bern, Switzerland

    Silvia Steila

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing AG

About this paper

Cite this paper

Pourmoradnasseri, M., Theis, D.O. (2017). Nondeterministic Communication Complexity of Random Boolean Functions (Extended Abstract). In: Gopal, T., Jäger , G., Steila, S. (eds) Theory and Applications of Models of Computation. TAMC 2017. Lecture Notes in Computer Science(), vol 10185. Springer, Cham. https://doi.org/10.1007/978-3-319-55911-7_38

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-55911-7_38

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-55910-0

  • Online ISBN: 978-3-319-55911-7

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation