An Algorithm for Koml\'os Conjecture Matching Banaszczyk's bound

10 Sep 2016  ·  Bansal Nikhil, Dadush Daniel, Garg Shashwat ·

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. read more

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Data Structures and Algorithms Discrete Mathematics

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