A non-algorithmic, generalized version of a recent result, asserting that a natural relaxation of the Komlós conjecture from boolean discrepancy to spherical discrepancy is true, is proved by a very short argument using convex geometry.

Here it is proved that if the columns of A are assigned unit real vectors rather than +/- 1 then the Komlos conjecture holds with K=1, which opens the way to proving tighter efficient (polynomial-time computable) upper bounds for the conjecture using semidefinite programming techniques.Expand

The algorithm is used to give the first non-trivial lower bounds for the problem of covering a hypersphere by hyperspherical caps of uniform volume at least $2^{-o(\sqrt{n})}$.Expand

Given n sets on n elements it is shown that there exists a two-coloring such that all sets have discrepancy at most Knl/2, K an absolute constant. This improves the basic probabilistic method with… Expand