Divide-and-approximate: a novel constraint push strategy for iceberg cube mining

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

doi:10.1109/tkde.2005.45

Cited by 9 publications

(20 citation statements)

References 19 publications

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“…The aggregate function F can be an SQL aggregate function or a commonly seen complex aggregate function such as Average (Avg) or Variance (Var). As will be shown later in our experiments on real-world and synthetic benchmark data sets, our BP-Cubing algorithms are several times faster than existing pruning techniques, including the most recent Divide-and-Approximate (DnA) algorithm [15].…”

Section: Introductionmentioning

confidence: 78%

“…Finally, we briefly discuss how our algorithms utilize antimonotone constraints. The iceberg cube with the constraint "Avg(Sale) in [15,20]" on the Sales data set in Table 1 is used as a running example throughout this section.…”

Section: Bound-prune Cubing Algorithmsmentioning

confidence: 99%

“…In G, the leaf nodes of the March subtree are the MSPs of CubeðSalesMan; CityÞjMarch. With the constraint "Avg(Sale) in [15,20]," G is pruned in constructing the subtree G p . By following Table 6, the bounds for CubeðSalesMan; CityÞjMarch are computed from the three leaf nodes originating from node (March) of G:…”

Section: Observation 4 With Top-down Aggregation Given a G-tree Gmentioning

confidence: 99%

“…As [2.5, 10] violates "Avg(Sale) in [15,20]," all three branches originating from (March) are removed from further computation. Similarly, Avg(Sale) of CubeðSalesman; CityÞjJanuary is bounded as [40,40], which violates the constraint, and is pruned.…”

Section: Observation 4 With Top-down Aggregation Given a G-tree Gmentioning

confidence: 99%

“…Computing iceberg cubes with such constraints has been a challenging problem. Existing proposals in the literature have all followed the approach of deriving weaker but antimonotone constraints [7], [15]. They are restricted in two aspects: 1) the weaker constraints derived from nonantimonotone constraints are often very loose and not effective enough for pruning, especially for complex constraints, and 2) aggregates are computed following the BUC framework, and only one group is aggregated at a time in the recursive partitioning process, which limits the amount of information readily available for pruning.…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Introductionmentioning

confidence: 78%

Section: Bound-prune Cubing Algorithmsmentioning

confidence: 99%

Section: Observation 4 With Top-down Aggregation Given a G-tree Gmentioning

confidence: 99%

Section: Observation 4 With Top-down Aggregation Given a G-tree Gmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Efficient Computation of Iceberg Cubes by Bounding Aggregate Functions

Zhang

Chou

Dong

2007

IEEE Trans. Knowl. Data Eng.

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Multiway Pruning for Efficient Iceberg Cubing

Zhang

Chou

2006

Lecture Notes in Computer Science

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Effective pruning is essential for efficient iceberg cube computation. Previous studies have focused on exclusive pruning: regions of a search space that do not satisfy some condition are excluded from computation. In this paper we propose inclusive and anti-pruning. With inclusive pruning, necessary conditions that solutions must satisfy are identified and regions that can not be reached by such conditions are pruned from computation. With anti-pruning, regions of solutions are identified and pruning is not applied. We propose the multiway pruning strategy combining exclusive, inclusive and anti-pruning with bounding aggregate functions in iceberg cube computation. Preliminary experiments demonstrate that the multiway-pruning strategy improves the efficiency of iceberg cubing algorithms with only exclusive pruning.

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Constrained pattern mining in the new era

Silva

Antunes

2015

Knowl Inf Syst

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Twenty years of research on frequent itemset mining, or pattern mining, has led to the existence of a set of efficient algorithms for identifying different types of patterns, from transactional to sequential. Despite the great advances in this field, big data brought a completely new context to operate, with new challenges arising from the growth in data size, dynamics and complexity. These challenges include the shift not only from static to dynamic data, but also from tabular to complex data sources, such as social networks (expressed as graphs) and data warehouses (expressed as multi-relational models). In this new context, and more than ever, users need effective ways to control the large number of discovered patterns, and to be able to choose what patterns to consider at each time. The most accepted and common approach to minimize these drawbacks has been to capture and represent the semantics of the domain through constraints, and use them not only to reduce the number of results, but also to focus the algorithms in areas where it is more likely to gain information and return more interesting results. The use of constraints in pattern mining has been widely studied, and there are a lot of proposed types of constraints and pushing strategies. In this paper, we present a new global view of the work done on the incorporation of constraints in the pattern mining process. In particular, we propose a new framework for constrained pattern mining, that allows us to organize and analyze existing algorithms and strategies, based on the different types and properties of constraints, and on the data sources they are able to handle.

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Divide-and-approximate: a novel constraint push strategy for iceberg cube mining

Cited by 9 publications

References 19 publications

Efficient Computation of Iceberg Cubes by Bounding Aggregate Functions

Efficient Computation of Iceberg Cubes by Bounding Aggregate Functions

Multiway Pruning for Efficient Iceberg Cubing

Constrained pattern mining in the new era

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