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.Yu Zhang, Hong Shen, Hui Tian and Xianchao Zhan