实用的熵压缩排序/选择字典
Practical Entropy-Compressed Rank/Select Dictionary
摘要：
排序/选择字典是用于计算$\rank(x,S)$的有序集$S \subset \{0,1,...,n-1\}$的数据结构（$S$中不大于$x$的元素数）和$\select(i,S)$（$i$ -$S$中的第小元素），它们是字符串、树、图等的\emph{succinct data structures}的基本组件。然而，在这些数据结构中，只考虑了渐近行为，它们对实际数据的性能并不令人满意。在本文中，我们提出了新的四个Rank/Select字典，esp，recrank，vcode和sdarray，其中每一个都是小的，如果$S$中的元素的数量是小的，并确实接近$nH_0(S)$（$H_0(S) \leq 1$是$S$的零阶\textit{empirical entropy}）在实践中，其查询时间优于以前的。实验结果揭示了我们的数据结构的特点，也表明，这些数据结构是优于现有的实现在规模和查询时间。
英文摘要：
Rank/Select dictionaries are data structures for an ordered set $S \subset \{0,1,...,n-1\}$ to compute $\rank(x,S)$ (the number of elements in $S$ which are no greater than $x$), and $\select(i,S)$ (the $i$-th smallest element in $S$), which are the fundamental components of \emph{succinct data structures} of strings, trees, graphs, etc. In those data structures, however, only asymptotic behavior has been considered and their performance for real data is not satisfactory. In this paper, we propose novel four Rank/Select dictionaries, esp, recrank, vcode and sdarray, each of which is small if the number of elements in $S$ is small, and indeed close to $nH_0(S)$ ($H_0(S) \leq 1$ is the zero-th order \textit{empirical entropy} of $S$) in practice, and its query time is superior to the previous ones. Experimental results reveal the characteristics of our data structures and also show that these data structures are superior to existing implementations in both size and query time.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
