Approximating Large Frequency Moments with Bits

In this paper we consider the problem of approximating frequency moments in the streaming model. Given a stream of numbers from , a frequency of is defined as . The -th\emph {frequency moment} of is defined as .In this paper we give an upper bound on the space required to find a -th frequency moment of bits that matches, up to a constant factor, the lower bound of Woodruff and Zhang (STOC 12) for constant and constant . Our algorithm makes a single pass over the stream and works for any constant .