Approximate Counting with a Floating-Point Counter

Memory becomes a limiting factor in contemporary applications, such as analyses of the Webgraph and molecular sequences, when many objects need to be counted simultaneously. Robert Morris [Communications of the ACM, 21:840–842, 1978] proposed a probabilistic technique for approximate counting that is extremely space-efficient. The basic idea is to increment a counter containing the value X with probability 2 . As a result, the counter contains an approximation of lgn after n probabilistic updates stored in lg lgn bits. Here we revisit the original idea of Morris, and introduce a binary floating-point counter that uses a d-bit significand in conjunction with a binary exponent. The counter yields a simple formula for an unbiased estimation of n with a standard deviation of about 0.6 · n2, and uses d + lg lg n bits. We analyze the floating-point counter’s performance in a general framework that applies to any probabilistic counter, and derive practical formulas to assess its accuracy. Department of Computer Science and Operations Research, Université de Montréal. Email: csuros AT iro.umontreal.ca