数据解析（Data Analytic），是指对数据集的属性值进行SUM，TopN，Rank，Select操作。一般要求实时响应。

集合（Set）

For a set of integers: S = {1, 2, 3, 1000}. Set operations:

tests: x ∈ S?

intersections: S1 ∩ S2

unions: S1 ∪ S2

differences: S1 ∖ S2

Jaccard Index (Tanimoto similarity) ∣S1 ∩ S2 ∣/∣S1 ∪ S2 ∣

有序集合（Ordered Set）

Iterate:

in sorted order,

in reverse order,

skippable iterators (jump to first value ≥ x)

Rank: how many elements of the set are smaller than k?

Select: find the kth smallest value

Min/max: find the maximal and minimal value

• Broadword Implementation of Rank

大数据解析平台，是实现数据解析的分布式软件系统。

• Apache Kylin
• Druid

1. Navarro, Gonzalo, and Eliana Providel. "Fast, small, simple rank/select on bitmaps." In International Symposium on Experimental Algorithms, pp. 295-306. Springer Berlin Heidelberg, 2012.
2. Vigna, Sebastiano. "Broadword implementation of rank/select queries." In International Workshop on Experimental and Efficient Algorithms, pp. 154-168. Springer Berlin Heidelberg, 2008.

基数估计（Cardinality Estimation），评估一个集合中不同数据项的个数的近似算法。比如，访问一个网站的独立IP个数。

• Cardinality Estimation Algorithm

1. Flajolet, Philippe, Éric Fusy, Olivier Gandouet, and Frédéric Meunier. "Hyperloglog: the analysis of a near-optimal cardinality estimation algorithm." DMTCS Proceedings 1 (2008).
2. Heule, Stefan, Marc Nunkesser, and Alexander Hall. "HyperLogLog in practice: algorithmic engineering of a state of the art cardinality estimation algorithm." In Proceedings of the 16th International Conference on Extending Database Technology, pp. 683-692. ACM, 2013.

关联规则挖掘（association rule mining），查找频繁项目集ItemSets。其中最有名的算法是Apriori算法。

基于位图的Apriori算法加速。

1. Kim, Sung-Tan, Jae-Myung Kim, and Sang-Won Lee. "BAR: bitmap-based association rule: an implementation and its optimizations." In Proceedings of the 7th International Conference on Advances in Mobile Computing and Multimedia, pp. 627-631. ACM, 2009.