Abstract
Many sketch data structures have been implemented. But due to our knowledge, the current sketching approach to summarizing the hierarchical structure in data was oracles-based, which stack logn sketches. By designing and using a XOR-based pair-wise independent family of hash functions on the hierarchical domain U*, a hierarchical sketch data structure was implemented to summarize the hierarchical structure in data stream, which mapped the data stream items to a three dimensional counter array of size LtimesDtimesW, of which, L was the number of layers in the hierarchical domain, D was the number of the hash functions chosen uniformly at random, and W was the range of the hash functions. The sketch used the breadth-first search strategy to identify and estimate the hierarchical frequent items online with user-specified probability. The experiments demonstrate substantial improvement in the update time and evaluating accuracy over the straightforward oracles-based sketch approach.
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