QuickSelect使用的符号比较数的分布收敛
Distributional convergence for the number of symbol comparisons used by QuickSelect
摘要：
当搜索算法QuickSelect在执行过程中比较键以找到目标排名的键时，它必须对键的表示或内部结构进行操作，而之前的研究根据数量量化了算法的执行成本，但忽略了这些内容。所需的键比较。在本文中，我们分析了运行成本的算法，不仅考虑到关键比较的数量，但每个关键比较的成本。我们假设键被表示为由各种概率源生成的符号序列，并且QuickSelect对单个符号进行操作以找到目标键。我们确定的限制分布的成本，并获得积分和系列表达式的期望的限制分布。这些表达式用于重新捕获先前获得的算法所需的关键比较次数的结果。
英文摘要：
When the search algorithm QuickSelect compares keys during its execution in order to find a key of target rank, it must operate on the keys' representations or internal structures, which were ignored by the previous studies that quantified the execution cost for the algorithm in terms of the number of required key comparisons. In this paper, we analyze running costs for the algorithm that take into account not only the number of key comparisons but also the cost of each key comparison. We suppose that keys are represented as sequences of symbols generated by various probabilistic sources and that QuickSelect operates on individual symbols in order to find the target key. We identify limiting distributions for the costs and derive integral and series expressions for the expectations of the limiting distributions. These expressions are used to recapture previously obtained results on the number of key comparisons required by the algorithm.
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