  We consider the problem of testing distribution identity. Given a sequence of
independent samples from an unknown distribution on a domain of size n, the
goal is to check if the unknown distribution approximately equals a known
distribution on the same domain. While Batu, Fortnow, Fischer, Kumar,
Rubinfeld, and White (FOCS 2001) proved that the sample complexity of the
problem is O~(sqrt(n) * poly(1/epsilon)), the running time of their tester is
much higher: O(n) + O~(sqrt(n) * poly(1/epsilon)). We modify their tester to
achieve a running time of O~(sqrt(n) * poly(1/epsilon)).
