An algorithm for Komlós Conjecture Matching Banaszczyk's bound

N. Bansal, D. Dadush, S. Garg

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We consider the problem of finding a low discrepancy coloring for sparse set systems where each element lies in at most t sets. We give an efficient algorithm that finds a coloring with discrepancy O((t log n)^{1/2}), matching the best known non-constructive bound for the problem due to Banaszczyk. The previous algorithms only achieved an O(t^{1/2} log n) bound. The result also extends to the more general Koml\'{o}s setting and gives an algorithmic O(log^{1/2} n) bound.
Original languageEnglish
Article number1605.02882
Number of pages20
Publication statusPublished - 10 May 2016


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