Deterministic Discrepancy Minimization

  • Nikhil Bansal
  • Joel Spencer
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6942)

Abstract

We derandomize a recent algorithmic approach due to Bansal [2] to efficiently compute low discrepancy colorings for several problems. In particular, we give an efficient deterministic algorithm for Spencer’s six standard deviations result [13], and to a find low discrepancy coloring for a set system with low hereditary discrepancy.

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References

  1. 1.
    Alon, N., Spencer, J.: The Probabilistic Method. John Wiley, Chichester (2000)CrossRefMATHGoogle Scholar
  2. 2.
    Bansal, N.: Constructive algorithm for discrepancy minimization. In: FOCS 2010 (2010)Google Scholar
  3. 3.
    Beck, J.: Roth’s estimate on the discrepancy of integer sequences is nearly sharp. Combinatorica 1, 319–325 (1981)MathSciNetCrossRefMATHGoogle Scholar
  4. 4.
    Beck, J., Sos, V.: Discrepancy theory. In: Graham, R.L., Grotschel, M., Lovasz, L. (eds.) Handbook of Combinatorics, pp. 1405–1446. North-Holland, Amsterdam (1995)Google Scholar
  5. 5.
    Chazelle, B.: The discrepancy method: randomness and complexity. Cambridge University Press, Cambridge (2000)CrossRefMATHGoogle Scholar
  6. 6.
    Engebretsen, L., Indyk, P., O’Donnell, R.: Derandomized dimensionality reduction with applications. In: SODA 2002, pp. 705–712 (2002)Google Scholar
  7. 7.
    Kim, J.H., Matousek, J., Vu, V.H.: Discrepancy After Adding A Single Set. Combinatorica 25(4), 499–501 (2005)MathSciNetCrossRefMATHGoogle Scholar
  8. 8.
    Matousek, J.: Geometric Discrepancy: An Illustrated Guide, Algorithms and Combinatorics, vol. 18. Springer, Heidelberg (1999)MATHGoogle Scholar
  9. 9.
    Matousek, J.: An Lp version of the Beck-Fiala conjecture. European Journal of Combinatorics 19(2), 175–182 (1998)MathSciNetCrossRefMATHGoogle Scholar
  10. 10.
    Mahajan, S., Ramesh, H.: Derandomizing Approximation Algorithms Based on Semidefinite Programming. SIAM J. Comput. 28(5), 1641–1663 (1999)MathSciNetCrossRefMATHGoogle Scholar
  11. 11.
    Raghavan, P.: Probabilistic construction of deterministic algorithms: approximating packing integer programs. J. of Computer and Systems Sciences 37, 130–143Google Scholar
  12. 12.
    Spencer, J.: Balancing Games. J. Comb. Theory, Ser. B 23(1), 68–74 (1977)Google Scholar
  13. 13.
    Spencer, J.: Six standard deviations suffice. Trans. Amer. Math. Soc. 289, 679–706 (1985)MathSciNetCrossRefMATHGoogle Scholar
  14. 14.
    Sivakumar, D.: Algorithmic Derandomization via Complexity Theory. In: IEEE Conference on Computational Complexity (2002)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Nikhil Bansal
    • 1
  • Joel Spencer
    • 2
  1. 1.IBM T.J. WatsonYorktown Hts.USA
  2. 2.New York UniversityNew YorkUSA

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