Space complexity of hierarchical heavy hitters in multi-dimensional data streams

Heavy hitters, which are items occurring with frequency above a given threshold, are an important aggregation and summary tool when processing data streams or data warehouses. Hierarchical heavy hitters (HHHs) have been introduced as a natural generalization for hierarchical data domains, including multi-dimensional data. An item x in a hierarchy is called a φ-HHH if its frequency after discounting the frequencies of all its descendant hierarchical heavy hitters exceeds φn, where φ is a user-specified parameter and n is the size of the data set. Recently, single-pass schemes have been proposed for computing φ-HHHs using space roughly O( 1 φ log(φn)). The frequency estimates of these algorithms, however, hold only for the total frequencies of items, and not the discounted frequencies; this leads to false positives because the discounted frequency can be significantly smaller than the total frequency. This paper attempts to explain the difficulty of finding hierarchical heavy h...

• Type: Conference
• Year: 2005
• Where: PODS
• Authors: John Hershberger, Nisheeth Shrivastava, Subhash Suri, Csaba D. Tóth
• Keywords: Data Stream, Database, Heavy Hitters, Hierarchical Heavy Hitters, PODS 2005