Range Aggregation With Set Selection

In the classic range aggregation problem, we have a set \($\) of objects such that, given an interval \($\), a query counts how many objects of \($\) are covered by \($\). Besides COUNT, the problem can also be defined with other aggregate functions, e.g., SUM, MIN, MAX and AVERAGE. This paper studies a novel variant of range aggregation, where an object can belong to multiple sets. A query (at runtime) picks any two sets, and aggregates on their intersection. More formally, let \($S_{1},\ldots, S_{m\) be \($\) sets of objects. Given distinct set ids \($\), \($\) and an interval \($\), a query reports how many objects in \($S_{i}\mathop{\rm\cap\kern 0pt}\displaylimits S_{j\) are covered by \($\). We call this problem range aggregation with set selection (RASS). Its hardness lies in that the pair \($(i, j\) can have \(${m\choose 2\) choices, rendering effective indexing a non-trivial task. The RASS problem can also be defined with other aggregate functions, and generalized so that a query chooses more than 2 sets. We develop a system called RASS to power this type of queries. Our system has excellent efficiency in both theory and practice. Theoretically, it consumes linear space, and achieves nearly-optimal query time. Practically, it outperforms existing solutions on real datasets by a factor up to an order of magnitude. The paper also features a rigorous theoretical analysis on the hardness of the RASS problem, which reveals invaluable insight into its characteristics.