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
Alon, N., Spencer, J.: The Probabilistic Method. John Wiley, Chichester (2000)
Bansal, N.: Constructive algorithm for discrepancy minimization. In: FOCS 2010 (2010)
Beck, J.: Roth’s estimate on the discrepancy of integer sequences is nearly sharp. Combinatorica 1, 319–325 (1981)
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)
Chazelle, B.: The discrepancy method: randomness and complexity. Cambridge University Press, Cambridge (2000)
Engebretsen, L., Indyk, P., O’Donnell, R.: Derandomized dimensionality reduction with applications. In: SODA 2002, pp. 705–712 (2002)
Kim, J.H., Matousek, J., Vu, V.H.: Discrepancy After Adding A Single Set. Combinatorica 25(4), 499–501 (2005)
Matousek, J.: Geometric Discrepancy: An Illustrated Guide, Algorithms and Combinatorics, vol. 18. Springer, Heidelberg (1999)
Matousek, J.: An Lp version of the Beck-Fiala conjecture. European Journal of Combinatorics 19(2), 175–182 (1998)
Mahajan, S., Ramesh, H.: Derandomizing Approximation Algorithms Based on Semidefinite Programming. SIAM J. Comput. 28(5), 1641–1663 (1999)
Raghavan, P.: Probabilistic construction of deterministic algorithms: approximating packing integer programs. J. of Computer and Systems Sciences 37, 130–143
Spencer, J.: Balancing Games. J. Comb. Theory, Ser. B 23(1), 68–74 (1977)
Spencer, J.: Six standard deviations suffice. Trans. Amer. Math. Soc. 289, 679–706 (1985)
Sivakumar, D.: Algorithmic Derandomization via Complexity Theory. In: IEEE Conference on Computational Complexity (2002)
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Bansal, N., Spencer, J. (2011). Deterministic Discrepancy Minimization. In: Demetrescu, C., Halldórsson, M.M. (eds) Algorithms – ESA 2011. ESA 2011. Lecture Notes in Computer Science, vol 6942. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-23719-5_35
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DOI: https://doi.org/10.1007/978-3-642-23719-5_35
Publisher Name: Springer, Berlin, Heidelberg
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