Cole的参数搜索技术实用化
Cole's Parametric Search Technique Made Practical
摘要：
参数搜索在几何算法中有着广泛的应用。Cole的改进提供了一种在运行时间中节省对数因子的方法，而不是使用标准方法。不幸的是，这种改进的代价是使已经复杂的算法变得更加复杂;因此，这种技术主要是理论上的兴趣。在本文中，我们提供了一个算法工程框架，该框架允许以简单和实用的方式概率地实现相同的渐近复杂度（即，适合实际应用）。我们的方法的主要思想是表明，快速排序的一个变体，称为boxsort，可以用来驱动比较，而不是使用排序网络，如复杂的AKS网络，或EREW并行排序算法，如相当复杂的并行归并排序算法。这导致随机优化算法的运行时间与使用Cole方法的运行时间匹配，具有高概率，同时也是实用的。我们将展示如何在实际实现中的一些几何算法，利用参数搜索的结果，并提供实验结果，证明该方法的实用性。
英文摘要：
Parametric search has been widely used in geometric algorithms. Cole's improvement provides a way of saving a logarithmic factor in the running time over what is achievable using the standard method. Unfortunately, this improvement comes at the expense of making an already complicated algorithm even more complex; hence, this technique has been mostly of theoretical interest. In this paper, we provide an algorithm engineering framework that allows for the same asymptotic complexity to be achieved probabilistically in a way that is both simple and practical (i.e., suitable for actual implementation). The main idea of our approach is to show that a variant of quicksort, known as boxsort, can be used to drive comparisons, instead of using a sorting network, like the complicated AKS network, or an EREW parallel sorting algorithm, like the fairly intricate parallel mergesort algorithm. This results in a randomized optimization algorithm with a running time matching that of using Cole's method, with high probability, while also being practical. We show how this results in practical implementations of some geometric algorithms utilizing parametric searching and provide experimental results that prove practicality of the method.
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