Version 3 changes: ----------------- -- Fixed some errors in the version 2 writeup of the proof of Theorem 25. The theorem conclusion is unchanged. In particular, the v2 proof took q = Theta(log(1/delta)/log(1/eps)) in the case s = Omega(1/eps) and looked at q items colliding. This makes no sense if q > s (which can happen depending on the relationship between eps, delta). Really one should take q = Theta(sqrt(eps*s)), which is Theta(log(1/delta)/log(1/eps)) for the largest setting of s, but not always. See the version 3 paper for details. (4/28/2011) ----------------- Version 2 changes: ----------------- -- Showed that the construction of [Dasgupta-Kumar-Sarlos, STOC 2010] requires sparsity Omega~(eps^{-1} * log^2(1/delta)). (4/14/2011) -- Gave a second new construction which achieves sparsity Theta(eps^{-1} * log(1/delta)). (4/14/2011) -- Changed the title to "Sparser Johnson-Lindenstrauss Transforms", since we now give two constructions. (4/14/2011)