The Number of Symbol Comparisons in QuickSort and QuickSelect

Abstract We revisit the classical QuickSort and QuickSelect algorithms, under a complexity model that fully takes into account the elementary comparisons between symbols composing the records to be processed. Our probabilistic models belong to a broad category of information 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 log2 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.

• Type: Conference
• Year: 2009
• Where: ICALP
• Authors: Brigitte Vallée, James Allen Fill, Julien Clément, Philippe Flajolet
• Keywords: Average-case Complexity, Classical Quicksort, ICALP 2009, Markov Sources, Theoretical Computer Science