文章基本信息

标题：A general framework for the realistic analysis of sorting and searching algorithms. Application to some popular algorithms
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作者：Julien Cl{\'e}ment ; Thu Hien Nguyen Thi ; Brigitte Vall{\'e}e 等
期刊名称：LIPIcs : Leibniz International Proceedings in Informatics
电子版ISSN：1868-8969
出版年度：2013
卷号：20
页码：598-609
DOI：10.4230/LIPIcs.STACS.2013.598
出版社：Schloss Dagstuhl -- Leibniz-Zentrum fuer Informatik
摘要：We describe a general framework for realistic analysis of sorting and searching algorithms, and we apply it to the average-case analysis of five basic algorithms: three sorting algorithms (QuickSort, InsertionSort, BubbleSort) and two selection algorithms (QuickMin and SelectionMin). Usually, the analysis deals with the mean number of key comparisons, but, here, we view keys as words produced by the same source, which are compared via their symbols in the lexicographic order. The "realistic" cost of the algorithm is now the total number of symbol comparisons performed by the algorithm, and, in this context, the average-case analysis aims to providee stimates for the mean number of symbol comparisons used by the algorithm. For sorting algorithms, and with respect to key comparisons, the average-case complexity of QuickSort is asymptotic to 2n log n, InsertionSort to n^2/4 and BubbleSort to n^2/2. With respect to symbol comparisons, we prove that their average-case complexity becomes Theta(n log^2n), Theta(n^2), Theta (n^2 log n). For selection algorithms, and with respect to key comparisons, the average-case complexity of QuickMin is asymptotic to 2n, of SelectionMin is n - 1. With respect to symbol comparisons, we prove that their average-case complexity remains Theta(n). In these five cases, we describe the dominant constants which exhibit the probabilistic behaviour of the source (namely, entropy, and various notions of coincidence) with respect to the algorithm.
关键词：Probabilistic analysis of algorithms; Sorting and searching algorithms; Pattern matching; Permutations; Information theory; Rice formula; Asymptotic e