一种压缩间隙的数据感知度量
A Compressed-Gap Data-Aware Measure
摘要：
在本文中，我们考虑的问题，有效地表示一个集$S$的$n$项目出的一个宇宙$U=\{0,...,u-1\}$，同时支持对它的一些操作。让$G=g_1...g_n$的间隙流与$S$，$gap$的比特大小时，与\emph{gap-encoding}编码，和$H_0(G)$的经验零阶熵。我们证明了（1）当$G$是高度可压缩的时，$nH_0(G)\in o(gap)$是可压缩的;（2）当$nH_0(G) \leq n\log(u/n) + n \leq uH_0(S)$是高度可压缩的时，$nH_0(G) \leq n\log(u/n) + n \leq uH_0(S)$是可压缩的。令$d$为$S$中元素之间的\emph{distinct}间隙长度的数目。我们首先提出了一种新的空间有效的零阶压缩表示的$S$采取$n(H_0(G)+1)+\mathcal O(d\log u)$位的空间。然后，我们描述了一个完全可索引的字典，支持\emph{rank}和\emph{select}查询在$\mathcal O(\log(u/n)+\log\log u)$的时间，同时需要渐近相同的空间，所提出的压缩表示的$S$。
英文摘要：
In this paper, we consider the problem of efficiently representing a set $S$ of $n$ items out of a universe $U=\{0,...,u-1\}$ while supporting a number of operations on it. Let $G=g_1...g_n$ be the gap stream associated with $S$, $gap$ its bit-size when encoded with \emph{gap-encoding}, and $H_0(G)$ its empirical zero-order entropy. We prove that (1) $nH_0(G)\in o(gap)$ if $G$ is highly compressible, and (2) $nH_0(G) \leq n\log(u/n) + n \leq uH_0(S)$. Let $d$ be the number of \emph{distinct} gap lengths between elements in $S$. We firstly propose a new space-efficient zero-order compressed representation of $S$ taking $n(H_0(G)+1)+\mathcal O(d\log u)$ bits of space. Then, we describe a fully-indexable dictionary that supports \emph{rank} and \emph{select} queries in $\mathcal O(\log(u/n)+\log\log u)$ time while requiring asymptotically the same space as the proposed compressed representation of $S$.
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。
