关系代数
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关系代数 (Relational Algebra)
集合运算
集合(Set)
For a set of integers: S = {1, 2, 3, 1000}. Set operations include:
membership test: x ∈ S?
Set intersection: S1 ∩ S2
Set union: S1 ∪ S2
Set 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? (counting the number of ones up to a given position)
- Select: find the kth smallest value (finding the position of the k-th bit set)
- Min/max: find the maximal and minimal value
Broadword Implementation of Rank/Select Queries
研究论文:
- Vigna, Sebastiano. "Broadword implementation of rank/select queries." In International Workshop on Experimental and Efficient Algorithms, WEA 2008.