Pushing aggregate constraints by divide-and-approximate

Wang, Ke; Jiang, Yuelong; Yu, Jeffrey Xu; Dong, Guozhu; Han, Jiawei

doi:10.1109/icde.2003.1260800

Cited by 7 publications

(11 citation statements)

References 10 publications

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“…Importantly, little overhead is incurred by bounding. Our experiments show that Bound-cubing is marginally more efficient than Star-cubing in computing iceberg cubes with monotone con-straints; it significantly outperforms the Divide and Approximate algorithm [9] for non-monotone constraints.…”

Section: Introductionmentioning

confidence: 94%

“…Divide and Approximate-cubing (D&A pruning) While bounding can handle some algebraic functions with local aggregations of both signs in × and / operations, they cannot be handled by D&A [9]. The constraint " SUM/MAX" cannot be approximated by D&A pruning when SUM and MAX can be both positive and negative values, but they can be bounded.…”

Section: Related Workmentioning

confidence: 99%

“…We discuss the two most related work, the Divide-and-Approximate [9] and Star-cubing [4] iceberg cubing algorithms.…”

Section: Related Workmentioning

confidence: 99%

“…Iceberg cubing for complex non-monotone constraints is challenging due to the difficulty of pruning. Recently, Wang et al [9] proposed an algorithm Divide and Approximate for pruning for non-monotone constraints. The pruning techniques however are only suitable for BUC like bottom-up single group oriented computation.…”

Section: Introductionmentioning

confidence: 99%

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Computing Complex Iceberg Cubes by Multiway Aggregation and Bounding

Chou

Zhang

2004

Data Warehousing and Knowledge Discovery

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Abstract. Iceberg cubing is a valuable technique in data warehouses. The efficiency of iceberg cube computation comes from efficient aggregation and effective pruning for constraints. In advanced applications, iceberg constraints are often non-monotone and complex, for example, "Average cost in the range [δ1, δ2] and standard deviation of cost less than β". The current cubing algorithms either are efficient in aggregation but weak in pruning for such constraints, or can prune for non-monotone constraints but are inefficient in aggregation. The best algorithm of the former, Star-cubing, computes aggregations of cuboids simultaneously but its pruning is specific to only monotone constraints such as "COUNT( * ) ≥ δ". In the latter case, the Divide and Approximate pruning technique can prune for non-monotone constraints but is limited to bottom-up single-group aggregation. We propose a solution that exhibits both efficiency in aggregation and generality and effectiveness in pruning for complex constraints. Our bounding techniques are as general as the Divide and Approximate pruning techniques for complex constraints and yet our multiway aggregation is as efficient as Star-cubing.

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Section: Introductionmentioning

confidence: 94%

Section: Related Workmentioning

confidence: 99%

“…We discuss the two most related work, the Divide-and-Approximate [9] and Star-cubing [4] iceberg cubing algorithms.…”

Section: Related Workmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Computing Complex Iceberg Cubes by Multiway Aggregation and Bounding

Chou

Zhang

2004

Data Warehousing and Knowledge Discovery

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“…Aggregates are computed during the construction of T s . Then, BPCubing is recursively called (lines [13][14], where group-bys of dimensions after B i are computed.…”

Section: The Top-down Bound-prune Cubing Algorithmmentioning

confidence: 99%

Efficient Computation of Iceberg Cubes by Bounding Aggregate Functions

Zhang

Chou

Dong

2007

IEEE Trans. Knowl. Data Eng.

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Abstract-The iceberg cubing problem is to compute the multidimensional group-by partitions that satisfy given aggregation constraints. Pruning unproductive computation for iceberg cubing when nonantimonotone constraints are present is a great challenge because the aggregate functions do not increase or decrease monotonically along the subset relationship between partitions. In this paper, we propose a novel bound prune cubing (BP-Cubing) approach for iceberg cubing with nonantimonotone aggregation constraints. Given a cube over n dimensions, an aggregate for any group-by partition can be computed from aggregates for the most specific n-dimensional partitions (MSPs). The largest and smallest aggregate values computed this way become the bounds for all partitions in the cube. We provide efficient methods to compute tight bounds for base aggregate functions and, more interestingly, arithmetic expressions thereof, from bounds of aggregates over the MSPs. Our methods produce tighter bounds than those obtained by previous approaches. We present iceberg cubing algorithms that combine bounding with efficient aggregation strategies. Our experiments on real-world and artificial benchmark data sets demonstrate that BP-Cubing algorithms achieve more effective pruning and are several times faster than state-of-the-art iceberg cubing algorithms and that BP-Cubing achieves the best performance with the top-down cubing approach.

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