Efficient temporal counting with bounded error

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 , a count-query retrieves the number of objects that are alive at q _t , and their keys fall in . We provide a method that accurately answers such queries, with error less than , 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.