An Algorithm for Komlós Conjecture Matching Banaszczyk's Bound

Nikhil Bansal, Daniel Dadush, Shashwat Garg
2016 2016 IEEE 57th Annual Symposium on Foundations of Computer Science (FOCS)  
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(log 1/2 n) bound.
doi:10.1109/focs.2016.89 dblp:conf/focs/BansalDG16 fatcat:hv26b5xfjzabvkfh52f5ipuig4