$S$ of objects such that, given an interval $I$ , a query counts how many objects of $S$ are covered by $I$ . 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 $m$ sets of objects. Given distinct set ids $i$ , $j$ and an interval $I$ , a query reports how many objects in $S_{i}\mathop{\rm\cap\kern 0pt}\displaylimits S_{j}$ are covered by $I$ . 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." /> $S$ of objects such that, given an interval $I$ , a query counts how many objects of $S$ are covered by $I$ . 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 $m$ sets of objects. Given distinct set ids $i$ , $j$ and an interval $I$ , a query reports how many objects in $S_{i}\mathop{\rm\cap\kern 0pt}\displaylimits S_{j}$ are covered by $I$ . 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." /> $S$ of objects such that, given an interval $I$ , a query counts how many objects of $S$ are covered by $I$ . 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 $m$ sets of objects. Given distinct set ids $i$ , $j$ and an interval $I$ , a query reports how many objects in $S_{i}\mathop{\rm\cap\kern 0pt}\displaylimits S_{j}$ are covered by $I$ . 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." /> Range Aggregation With Set Selection
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Issue No.05 - May (2014 vol.26)
pp: 1
Jong-Ryul Lee , , Korea Advanced Institute of Science and Technology, Daejeon, Republic of Korea
ABSTRACT
In the classic range aggregation problem, we have a set $S$ of objects such that, given an interval $I$ , a query counts how many objects of $S$ are covered by $I$ . 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 $m$ sets of objects. Given distinct set ids $i$ , $j$ and an interval $I$ , a query reports how many objects in $S_{i}\mathop{\rm\cap\kern 0pt}\displaylimits S_{j}$ are covered by $I$ . 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.
INDEX TERMS
Silicon, Aggregates, Arrays, Facebook, Aging, Indexing,Theory, Range Aggregation, Index
CITATION
Jong-Ryul Lee, "Range Aggregation With Set Selection", IEEE Transactions on Knowledge & Data Engineering, vol.26, no. 5, pp. 1, May 2014, doi:10.1109/TKDE.2013.125
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