表示序列的最优上下界
Optimal Lower and Upper Bounds for Representing Sequences
摘要：
支持查询$access$、$select$和$rank$的序列表示是许多数据结构的核心。对于这种表示，在各种上界和少数下界之间存在相当大的差距，以及它们与所使用的空间的关系。在这篇文章中，我们证明了$rank$，而允许使用的空间上的假设，并给出匹配的上界，只需要一个压缩表示的序列强下界。在此压缩空间内，运算$access$和$select$可以在恒定或几乎恒定的时间内求解，这对于大字母表是最佳的。我们的新的上界支配所有以前的工作中的时间/空间地图。
英文摘要：
Sequence representations supporting queries $access$, $select$ and $rank$ are at the core of many data structures. There is a considerable gap between the various upper bounds and the few lower bounds known for such representations, and how they relate to the space used. In this article we prove a strong lower bound for $rank$, which holds for rather permissive assumptions on the space used, and give matching upper bounds that require only a compressed representation of the sequence. Within this compressed space, operations $access$ and $select$ can be solved in constant or almost-constant time, which is optimal for large alphabets. Our new upper bounds dominate all of the previous work in the time/space map.
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。
