Dynamically Maintaining Duplicate-Insensitive and Time-Decayed Sum Using Time-Decaying Bloom Filter

The duplicate-insensitive and time-decayed sum of an arbitrary subset in a stream is an important aggregation for various analyses in many distributed stream scenarios. In general, precisely providing this sum in an unbounded and high-rate stream is infeasible. Therefore, we target at this problem and introduce a sketch, namely, time-decaying Bloom Filter (TDBF). The TDBF can detect duplicates in a stream and meanwhile dynamically maintain decayed-weight of all distinct elements in the stream according to a user-specified decay function. For a query for the current decayed sum of a subset in the stream, TDBF provides an effective estimation. In our theoretical analysis, a provably approximate guarantee has been given for the error of the estimation. In addition, the experimental results on synthetic stream validate our theoretical analysis.