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arXiv · 1605.02882

An Algorithm for Komlós Conjecture Matching Banaszczyk's bound

Nikhil Bansal·Daniel Dadush·Shashwat Garg
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Abstract

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 Komlós setting and gives an algorithmic O(log^{1/2} n) bound.

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Nikhil Bansal, Daniel Dadush, Shashwat Garg. 2016-09-10. An Algorithm for Komlós Conjecture Matching Banaszczyk's bound. https://arxiv.org/abs/1605.02882

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