An algorithm for komlós conjecture matching Banaszczyk's bound

\u3cp\u3e 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((tlog n) \u3csup\u3e1\u3c/sup\u3e / \u3csup\u3e2\u3c/sup\u3e ), matching the best known nonconstructive bound for the problem due to Banaszczyk. The previous algorithms only achieved an O(t \u3csup\u3e1\u3c/sup\u3e / \u3csup\u3e2\u3c/sup\u3e log n) bound. The result also extends to the more general Komlós setting and gives an algorithmic O(log \u3csup\u3e1\u3c/sup\u3e / \u3csup\u3e2\u3c/sup\u3e n) bound. \u3c/p\u3

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(t1/2 log n) bound. The result also extends to the more general Komlós setting and gives an algorithmic O(log1/2n) bound