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Conference Papers Year : 2009

The Number of Symbol Comparisons in QuickSort and QuickSelect

Abstract

We revisit the classical QuickSort and QuickSelect algo-rithms, under a complexity model that fully takes into account the ele-mentary comparisons between symbols composing the records to be pro-cessed. Our probabilistic models belong to a broad category of informa-tion sources that encompasses memoryless (i.e., independent-symbols) and Markov sources, as well as many unbounded-correlation sources. We establish that, under our conditions, the average-case complexity of QuickSort is O(n log 2 n) [rather than O(n log n), classically], whereas that of QuickSelect remains O(n). Explicit expressions for the implied constants are provided by our combinatorial–analytic methods.
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Dates and versions

hal-01082394 , version 1 (13-11-2014)

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Brigitte Vallée, Julien Clément, James Allen Fill, Philippe Flajolet. The Number of Symbol Comparisons in QuickSort and QuickSelect. 36th International Colloquium on Automata, Languages and Programming, Jul 2009, Rhodes, Greece. pp.750 - 763, ⟨10.1007/978-3-642-02927-1_62⟩. ⟨hal-01082394⟩
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