Efficient Evaluation of Sparse Data Cubes

Computing data cubes requires the aggregation of measures over arbitrary combinations of dimensions in a data set. Efficient data cube evaluation remains challenging because of the potentially very large sizes of input datasets (e.g., in the data warehousing context), the well-known curse of dimensionality, and the complexity of queries that need to be supported. This paper proposes a new dynamic data structure called SST (Sparse Statistics Trees) and a novel, in-teractive, and fast cube evaluation algorithm called CUPS (Cubing by Pruning SST), which is especially well suitable for computing aggregates in cubes whose data sets are sparse. SST only stores the aggregations of non-empty cube cells instead of the detailed records. Furthermore, it retains in memory the dense cubes (a.k.a. iceberg cubes) whose aggregate values are above a threshold. Sparse cubes are stored on disks. This allows a fast, accurate approximation for queries. If users desire more refined answers, related sparse cubes are aggregated. SST is incrementally maintainable, which makes CUPS suitable for data warehousing and analysis of streaming data. Experiment results demonstrate the excellent performance and good scalability of our approach

Efficient Evaluation of Sparse Data Cubes

available at www.springerlink.com ***Note: Figures may be missing from this format of the document Computing data cubes requires the aggregation of measures over arbitrary combinations of dimensions in a data set. Efficient data cube evaluation remains challenging because of the potentially very large sizes of input datasets (e.g., in the data warehousing context), the well-known curse of dimensionality, and the complexity of queries that need to be supported. This paper proposes a new dynamic data structure called SST (Sparse Statistics Trees) and a novel, in-teractive, and fast cube evaluation algorithm called CUPS (Cubing by Pruning SST), which is especially well suitable for computing aggregates in cubes whose data sets are sparse. SST only stores the aggregations of non-empty cube cells instead of the detailed records. Furthermore, it retains in memory the dense cubes (a.k.a. iceberg cubes) whose aggregate values are above a threshold. Sparse cubes are stored on disks. This allows a fast, accurate approximation for queries. If users desire more refined answers, related sparse cubes are aggregated. SST is incrementally maintainable, which makes CUPS suitable for data warehousing and analysis of streaming data. Experiment results demonstrate the excellent performance and good scalability of our approach. Article

How to evaluate multiple range-sum queries progressively

Decision support system users typically submit batches of range-sum queries simultaneously rather than issuing individual, unrelated queries. We propose a wavelet based technique that exploits I/O sharing across a query batch to evaluate the set of queries progressively and efficiently. The challenge is that now controlling the structure of errors across query results becomes more critical than minimizing error per individual query. Consequently, we define a class of structural error penalty functions and show how they are controlled by our technique. Experiments demonstrate that our technique is efficient as an exact algorithm, and the progressive estimates are accurate, even after less than one I/O per query

Attribute Value Reordering For Efficient Hybrid OLAP

The normalization of a data cube is the ordering of the attribute values. For large multidimensional arrays where dense and sparse chunks are stored differently, proper normalization can lead to improved storage efficiency. We show that it is NP-hard to compute an optimal normalization even for 1x3 chunks, although we find an exact algorithm for 1x2 chunks. When dimensions are nearly statistically independent, we show that dimension-wise attribute frequency sorting is an optimal normalization and takes time O(d n log(n)) for data cubes of size n^d. When dimensions are not independent, we propose and evaluate several heuristics. The hybrid OLAP (HOLAP) storage mechanism is already 19%-30% more efficient than ROLAP, but normalization can improve it further by 9%-13% for a total gain of 29%-44% over ROLAP

PolyFit: Polynomial-based Indexing Approach for Fast Approximate Range Aggregate Queries

Range aggregate queries find frequent application in data analytics. In some use cases, approximate results are preferred over accurate results if they can be computed rapidly and satisfy approximation guarantees. Inspired by a recent indexing approach, we provide means of representing a discrete point data set by continuous functions that can then serve as compact index structures. More specifically, we develop a polynomial-based indexing approach, called PolyFit, for processing approximate range aggregate queries. PolyFit is capable of supporting multiple types of range aggregate queries, including COUNT, SUM, MIN and MAX aggregates, with guaranteed absolute and relative error bounds. Experiment results show that PolyFit is faster and more accurate and compact than existing learned index structures.Comment: 13 page

Histograms and Wavelets on Probabilistic Data

There is a growing realization that uncertain information is a first-class citizen in modern database management. As such, we need techniques to correctly and efficiently process uncertain data in database systems. In particular, data reduction techniques that can produce concise, accurate synopses of large probabilistic relations are crucial. Similar to their deterministic relation counterparts, such compact probabilistic data synopses can form the foundation for human understanding and interactive data exploration, probabilistic query planning and optimization, and fast approximate query processing in probabilistic database systems. In this paper, we introduce definitions and algorithms for building histogram- and wavelet-based synopses on probabilistic data. The core problem is to choose a set of histogram bucket boundaries or wavelet coefficients to optimize the accuracy of the approximate representation of a collection of probabilistic tuples under a given error metric. For a variety of different error metrics, we devise efficient algorithms that construct optimal or near optimal B-term histogram and wavelet synopses. This requires careful analysis of the structure of the probability distributions, and novel extensions of known dynamic-programming-based techniques for the deterministic domain. Our experiments show that this approach clearly outperforms simple ideas, such as building summaries for samples drawn from the data distribution, while taking equal or less time