The predecessor problem is a key component of the fundamental sorting-and-searching core of algorithmic problems. While binary search is the optimal solution in the comparison model, more realistic machine models on integer sets open the door to a rich universe of data structures, algorithms, and lower bounds. In this article, we review the evolution of the solutions to the predecessor problem, focusing on the important algorithmic ideas, from the famous data structure of van Emde Boas to the optimal results of Patrascu and Thorup. We also consider lower bounds, variants, and special cases, as well as the remaining open questions.

中文翻译：

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前身搜索

这前任问题是算法问题的基本排序和搜索核心的关键组成部分。虽然二分搜索是比较模型中的最佳解决方案，但整数集上更真实的机器模型为丰富的数据结构、算法和下界打开了大门。在本文中，我们回顾了前一问题的解决方案的演变，重点介绍了重要的算法思想，从著名的 van Emde Boas 数据结构到 Patrascu 和 Thorup 的最优结果。我们还考虑了下界、变体和特殊情况，以及剩余的未解决问题。