动态随机集的工程前置数据结构
Engineering Predecessor Data Structures for Dynamic Integer Sets
摘要：
我们提出了高度优化的数据结构的动态前任问题，其中的任务是保持一组$S$的$w$位数下插入，删除，和前任查询（返回最大的元素$S$不大于一个给定的键）。寻找前趋问题可以被看作是成员问题的一种推广形式，或者是最近邻问题的一个简单版本。它是各种现实问题的核心，例如互联网路由。在这项工作中，我们设计了（1）宇宙简化思想的简单实现，类似于van-Emde-Boas树（2）y-快速尝试的变体[Willard，IPL'83]，以及（3）具有不同策略的B-树，用于组织节点中包含的密钥，包括动态融合节点的实现[Pintrachecu和Thorup，FOCS'14]。我们为$w=32,40,64$实现了我们的数据结构，它涵盖了大多数典型的场景。我们的数据结构比以前的方法更快地完成工作负载，同时空间效率更高，例如，它们的性能明显优于STL的标准实现，因为它们使用不到三分之一的内存完成的速度是标准实现的四倍。我们的测试还提供了关于数据结构设计的更一般的见解，例如应该如何存储和处理小集合，以及新的CPU指令（如高级向量扩展）是否以及何时获得回报。
英文摘要：
We present highly optimized data structures for the dynamic predecessor problem, where the task is to maintain a set $S$ of $w$-bit numbers under insertions, deletions, and predecessor queries (return the largest element in $S$ no larger than a given key). The problem of finding predecessors can be viewed as a generalized form of the membership problem, or as a simple version of the nearest neighbour problem. It lies at the core of various real-world problems such as internet routing. In this work, we engineer (1) a simple implementation of the idea of universe reduction, similar to van-Emde-Boas trees (2) variants of y-fast tries [Willard, IPL'83], and (3) B-trees with different strategies for organizing the keys contained in the nodes, including an implementation of dynamic fusion nodes [Pǎtraşcu and Thorup, FOCS'14]. We implement our data structures for $w=32,40,64$, which covers most typical scenarios. Our data structures finish workloads faster than previous approaches while being significantly more space-efficient, e.g., they clearly outperform standard implementations of the STL by finishing up to four times as fast using less than a third of the memory. Our tests also provide more general insights on data structure design, such as how small sets should be stored and handled and if and when new CPU instructions such as advanced vector extensions pay off.
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。
