位图上的阈值函数和对称函数
Threshold and Symmetric Functions over Bitmaps
摘要：
位图索引通常用于加速数据库中的简单聚合查询。交集、并和补等集合运算可以表示为逻辑运算（AND、OR、NOT）。然而，对于位图索引在更高级的查询中的应用知之甚少。我们希望扩展位图索引的适用性。作为起点，我们考虑对称布尔查询（例如，阈值函数）。例如，我们可能会将商店视为一组产品，并要求在2到10家商店中销售的产品。这种对称布尔查询推广了交集、并集和T出现查询。对于工程师来说，如何将位图索引用于对称布尔查询可能不是显而易见的。然而，也许令人惊讶的是，我们发现，我们最好的基于位图的算法与最先进的算法在重要的特殊情况下（例如，MergeOpt、MergeSkip、DivideSkip、ScanCount）。此外，与竞争算法不同，我们的计算结果再次是一个位图，可以在位图索引中进一步处理。我们检讨算法设计问题，如许多压缩位图的聚合。最后，我们讨论了位图索引可能能够有效支持的其他高级查询。
英文摘要：
Bitmap indexes are routinely used to speed up simple aggregate queries in databases. Set operations such as intersections, unions and complements can be represented as logical operations (AND, OR, NOT). However, less is known about the application of bitmap indexes to more advanced queries. We want to extend the applicability of bitmap indexes. As a starting point, we consider symmetric Boolean queries (e.g., threshold functions). For example, we might consider stores as sets of products, and ask for products that are on sale in 2 to 10 stores. Such symmetric Boolean queries generalize intersection, union, and T-occurrence queries. It may not be immediately obvious to an engineer how to use bitmap indexes for symmetric Boolean queries. Yet, maybe surprisingly, we find that the best of our bitmap-based algorithms are competitive with the state-of-the-art algorithms for important special cases (e.g., MergeOpt, MergeSkip, DivideSkip, ScanCount). Moreover, unlike the competing algorithms, the result of our computation is again a bitmap which can be further processed within a bitmap index. We review algorithmic design issues such as the aggregation of many compressed bitmaps. We conclude with a discussion on other advanced queries that bitmap indexes might be able to support efficiently.
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