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

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 (nlgn) comparisons on average. © 2007 Elsevier B.V. All rights reserved.

• Type: Journal
• Year: 2007
• Where: IPL
• Authors: Brendan Lucier, Tao Jiang, Ming Li
• Keywords: Binary Insertion Tree, Encoding Scheme, IPL 2007, Succinct Encoding Scheme