License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.APPROX-RANDOM.2014.258
URN: urn:nbn:de:0030-drops-47014
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2014/4701/
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Harvey, Nicholas J. A. ; Schwartz, Roy ; Singh, Mohit

Discrepancy Without Partial Colorings

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Abstract

Spencer's theorem asserts that, for any family of n subsets of ground set of size n, the elements of the ground set can be "colored" by the values +1 or -1 such that the sum of every set is O(sqrt(n)) in absolute value. All existing proofs of this result recursively construct "partial colorings", which assign +1 or -1 values to half of the ground set. We devise the first algorithm for Spencer's theorem that directly computes a coloring, without recursively computing partial colorings.

BibTeX - Entry

@InProceedings{harvey_et_al:LIPIcs:2014:4701,
  author =	{Nicholas J. A. Harvey and Roy Schwartz and Mohit Singh},
  title =	{{Discrepancy Without Partial Colorings}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2014)},
  pages =	{258--273},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-74-3},
  ISSN =	{1868-8969},
  year =	{2014},
  volume =	{28},
  editor =	{Klaus Jansen and Jos{\'e} D. P. Rolim and Nikhil R. Devanur and Cristopher Moore},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2014/4701},
  URN =		{urn:nbn:de:0030-drops-47014},
  doi =		{10.4230/LIPIcs.APPROX-RANDOM.2014.258},
  annote =	{Keywords: Combinatorial Discrepancy, Brownian Motion, Semi-Definite Programming, Randomized Algorithm}
}

Keywords: Combinatorial Discrepancy, Brownian Motion, Semi-Definite Programming, Randomized Algorithm
Collection: Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2014)
Issue Date: 2014
Date of publication: 04.09.2014

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