编码范围前2查询的实际实现

Seungbum Jo, Wooyoung Park, S. Rao
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引用次数: 0

摘要

我们为范围Top-2查询(RT2Q)设计了一种实用的编码变体,并评估了其性能。给定一个数组$A[1,n]$,包含总顺序为$n的$n个元素,范围Top-2编码问题是构造一个回答${\textsf{RT2Q}}{}$的数据结构,它返回$A$给定范围内第一大和第二大元素的位置,而不需要在查询时访问数组$A$。我们设计了以下两种实现:(i)基于Davoodi等人的替代表示的实现。反式。皇家Soc。[A, 2016]数据结构,有效支持查询。实验结果表明,我们的实现在实践中是有效的,并且与索引数据结构(保留原始数组$A$作为数据结构的一部分)相比,在范围最大查询中提供了更好的时间-空间权衡。(ii)基于Jo等人在$2 \times n$数组上的${\textsf{RT2Q}}{}$编码的另一种实现[CPM, 2016],可以在$O(n)$ time内构造。我们将我们的编码与Gawrychowski和Nicholson的最优编码[ICALP, 2015]进行了比较,并表明在大多数情况下,我们的编码在实践中使用竞争空间时显示出更快的构建时间。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Practical Implementation of Encoding Range Top-2 Queries
We design a practical variant of an encoding for range Top-2 query (RT2Q) and evaluate its performance. Given an array $A[1,n]$ of $n$ elements from a total order, the range Top-2 encoding problem is to construct a data structure that answers ${\textsf{RT2Q}}{}$, which returns the positions of the first and second largest elements within a given range of $A$, without accessing the array $A$ at query time. We design the following two implementations: (i) an implementation based on an alternative representation of Davoodi et al.’s [Phil. Trans. Royal Soc. A, 2016] data structure, which supports queries efficiently. Experimental results show that our implementation is efficient in practice and gives improved time-space trade-offs compared with the indexing data structures (which keep the original array $A$ as part of the data structure) for range maximum queries. (ii) Another implementation based on Jo et al.’s ${\textsf{RT2Q}}{}$ encoding on $2 \times n$ array [CPM, 2016], which can be constructed in $O(n)$ time. We compare our encoding with Gawrychowski and Nicholson’s optimal encoding [ICALP, 2015] and show that in most cases, our encoding shows faster construction time while using a competitive space in practice.
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