Efficient temporal counting with bounded error

  • Authors:

  • Yufei Tao;Xiaokui Xiao

  • Affiliations:

  • Department of Computer Science and Engineering, Chinese University of Hong Kong, New Territories, Hong Kong;Department of Computer Science and Engineering, Chinese University of Hong Kong, New Territories, Hong Kong

  • Venue:
  • The VLDB Journal — The International Journal on Very Large Data Bases
  • Year:
  • 2008

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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 驴 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.