An Algorithm for Komlós Conjecture Matching Banaszczyk's Bound
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چکیده
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)), matching the best known non-constructive bound for the problem due to Banaszczyk. The previous algorithms only achieved an O(t log n) bound. Our result also extends to the more general Komlós setting and gives an algorithmic O(log n) bound.
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تاریخ انتشار 2016