基排序和马尔可夫输入尝试的一个极限定理
A Limit Theorem for Radix Sort and Tries with Markovian Input
摘要：
Tries是单词上最通用和最广泛使用的数据结构之一。特别是，它们被用于基本的排序算法，如基数排序，我们在本文中研究。虽然基数排序和尝试的性能在一个现实的概率模型下产生的话是非常重要的，它的分析，即使是最简单的无记忆信源，已被证明是困难的。在本文中，我们考虑一个更现实的模型，其中的话是由一个马尔可夫信源。通过一种新的使用收缩方法结合矩转移技术，我们证明了一个中心极限定理的基数排序的复杂性和外部路径长度的trie。这是第一次应用的收缩方法的分析算法和数据结构与马尔可夫输入;它依赖于使用系统的随机递归结合产品版本的Zolotarev度量。
英文摘要：
Tries are among the most versatile and widely used data structures on words. In particular, they are used in fundamental sorting algorithms such as radix sort which we study in this paper. While the performance of radix sort and tries under a realistic probabilistic model for the generation of words is of significant importance, its analysis, even for simplest memoryless sources, has proved difficult. In this paper we consider a more realistic model where words are generated by a Markov source. By a novel use of the contraction method combined with moment transfer techniques we prove a central limit theorem for the complexity of radix sort and for the external path length in a trie. This is the first application of the contraction method to the analysis of algorithms and data structures with Markovian inputs; it relies on the use of systems of stochastic recurrences combined with a product version of the Zolotarev metric.
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