最优排序演化数据
Optimally Sorting Evolving Data
摘要：
我们给出了最优排序算法在不断发展的数据框架，其中一个算法的输入数据是不断变化的，而算法的执行。在这个框架中，算法不是产生最终输出，而是试图保持输出接近数据当前状态的正确输出，随着时间的推移重复更新其正确输出的最佳估计。我们表明，一个简单的重复插入-排序算法可以保持一个O（n）的Kendall tau距离，具有很高的概率，在一个不断发展的数据模型中，每个比较之后是一个随机的连续对项目之间的交换，在底层的总顺序的n个项目之间的维护列表和底层的总顺序。这个结果是渐近最优的，因为这个问题的Kendall tau距离存在一个Omega（n）下界。我们的结果关闭了这个下限和以前的最佳算法之间的差距，这个问题，它保持了一个Kendall tau距离O（n log log n）的高概率。这也证实了以前的实验结果表明，插入排序往往比快速排序在实践中表现得更好。
英文摘要：
We give optimal sorting algorithms in the evolving data framework, where an algorithm's input data is changing while the algorithm is executing. In this framework, instead of producing a final output, an algorithm attempts to maintain an output close to the correct output for the current state of the data, repeatedly updating its best estimate of a correct output over time. We show that a simple repeated insertion-sort algorithm can maintain an O(n) Kendall tau distance, with high probability, between a maintained list and an underlying total order of n items in an evolving data model where each comparison is followed by a swap between a random consecutive pair of items in the underlying total order. This result is asymptotically optpimal, since there is an Omega(n) lower bound for Kendall tau distance for this problem. Our result closes the gap between this lower bound and the previous best algorithm for this problem, which maintains a Kendall tau distance of O(n log log n) with high probability. It also confirms previous experimental results that suggested that insertion sort tends to perform better than quicksort in practice.
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