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.
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Conference Annual IEEE Symposium on Foundations of Computer Science
Citation
Bansal, N, Dadush, D.N, & Garg, S. (2016). An algorithm for Komlós Conjecture matching Banaszczyk’s Bound. In Proceedings of Annual IEEE Symposium on Foundations of Computer Science 2016 (FOCS 57).