In order to avoid the redundant and inconsistent information in distributed data streams, a sampling method based on min-wise hash functions is designed and the practical semantics of the union of distributed data streams is defined. First, for each family of min-wise hash functions, the data with the minimum hash value are selected as local samples and the biased effect caused by frequent updates in a single data stream is filtered out. Secondly, for the same hash function, the sample with the minimum hash value is selected as the global sample and the local samples are combined at the center node to filter out the biased effect of duplicated updates. Finally, based on the obtained uniform samples, several aggregations on the defined semantics of the union of data streams are precisely estimated. The results of comparison tests on synthetic and real-life data streams demonstrate the effectiveness of this method.
