An algorithm for Komlós conjecture matching Banaszczyk's bound

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 nonconstructive 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(log1/2n) bound.}