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Efficient temporal counting with bounded error

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Abstract

This paper studies aggregate search in transaction time databases. Specifically, each object in such a database can be modeled as a horizontal segment, whose y-projection is its search key, and its x-projection represents the period when the key was valid in history. Given a query timestamp q t and a key range \(\vec{q_k}\) , a count-query retrieves the number of objects that are alive at q t , and their keys fall in \(\vec{q_k}\) . We provide a method that accurately answers such queries, with error less than \(\frac{1}{\varepsilon} + \varepsilon \cdot N_{\rm alive}(q_t)\) , where N alive(q t ) is the number of objects alive at time q t , and ɛ is any constant in (0, 1]. Denoting the disk page size as B, and n =  N / B, our technique requires O(n) space, processes any query in O(log B n) time, and supports each update in O(log B n) amortized I/Os. As demonstrated by extensive experiments, the proposed solutions guarantee query results with extremely high precision (median relative error below 5%), while consuming only a fraction of the space occupied by the existing approaches that promise precise results.

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Authors and Affiliations

  1. Department of Computer Science and Engineering, Chinese University of Hong Kong, New Territories, Hong Kong

    Yufei Tao & Xiaokui Xiao

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  1. Yufei Tao
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  2. Xiaokui Xiao
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Correspondence to Yufei Tao.

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Tao, Y., Xiao, X. Efficient temporal counting with bounded error. The VLDB Journal 17, 1271–1292 (2008). https://doi.org/10.1007/s00778-007-0066-x

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