document: Exploiting duality in summarization with deterministic guarantees Summarization is an important task in data mining . A major challenge over the past years has been the efficient construction of fixed-space synopses that provide a deterministic quality guarantee , often expressed in terms of a maximum-error metric . Histograms and several hierarchical techniques have been proposed for this problem . However , their time and\/or space complexities remain impractically high and depend not only on the data set size n , but also on the space budget B. These handicaps stem from a requirement to tabulate all allocations of synopsis space to different regions of the data . In this paper we develop an alternative methodology that dispels these deficiencies , thanks to a fruitful application of the solution to the dual problem : given a maximum allowed error , determine the minimum-space synopsis that achieves it . Compared to the state-of-the-art , our histogram construction algorithm reduces time complexity by ( at least ) a Blog2n over logε \* factor and our hierarchical synopsis algorithm reduces the complexity by ( at least ) a factor of log2B over logε \* + logn in time and B ( 1-log B over log n ) in space , where ε \* is the optimal error . These complexity advantages offer both a space-efficiency and a scalability that previous approaches lacked . We verify the benefits of our approach in practice by experimentation .
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