Average-case analysis of QuickSort and Binary Insertion Tree height using incompressibility

Authors:
Brendan Lucier;Tao Jiang;Ming Li
Affiliations:
Department of Computer Science, University of Waterloo, Waterloo, Ont. N2L 3G1, Canada;Department of Compute Science, University of California, Riverside, CA 92521, USA;Department of Computer Science, University of Waterloo, Waterloo, Ont. N2L 3G1, Canada
Venue:
Information Processing Letters
Year:
2007

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Abstract

We study the Kolmogorov complexity of a Binary Insertion Tree, and present a succinct encoding scheme for Binary Insertion Trees produced from incompressible permutations. Based on the encoding scheme, we obtain a simple incompressibility argument that yields an asymptotic analysis of the average height of a Binary Insertion Tree. This argument further implies that the QuickSort algorithm sorts a permutation of n elements in @Q(nlgn) comparisons on average.