Flexible approximate counting

Approximate counting [18] is useful for data stream and database summarization. It can help in many settings that allow only one pass over the data, want low memory usage, and can accept some relative error. Approximate counters use fewer bits; we focus on 8-bits but our results are general. These small counters represent a sparse sequence of larger numbers. Counters are incremented probabilistically based on the spacing between the numbers they represent. Our contributions are a customized distribution of counter values and efficient strategies for deciding when to increment them. At run-time, users may independently select the spacing (accuracy) of the approximate counter for small, medium, and large values. We allow the user to select the maximum number to count up to, and our algorithm will select the exponential base of the spacing. These provide additional flexibility over both classic and Csűrös's [4] floating-point approximate counting. These provide additional structure, a useful schema for users, over Kruskal and Greenberg [13]. We describe two new and efficient strategies for incrementing approximate counters: use a deterministic countdown or sample from a geometric distribution. In Csűrös all increments are powers of two, so random bits rather than full random numbers can be used. We also provide the option to use powers-of-two but retain flexibility. We show when each strategy is fastest in our implementation.