Dual-Pivot Quicksort: Optimality, Analysis and Zeros of Associated Lattice Paths
Combinatorics
2019-11-11 v2 Data Structures and Algorithms
Abstract
We present an average case analysis of a variant of dual-pivot quicksort. We show that the used algorithmic partitioning strategy is optimal, i.e., it minimizes the expected number of key comparisons. For the analysis, we calculate the expected number of comparisons exactly as well as asymptotically, in particular, we provide exact expressions for the linear, logarithmic, and constant terms. An essential step is the analysis of zeros of lattice paths in a certain probability model. Along the way a combinatorial identity is proven.
Keywords
Cite
@article{arxiv.1611.00258,
title = {Dual-Pivot Quicksort: Optimality, Analysis and Zeros of Associated Lattice Paths},
author = {Martin Aumüller and Martin Dietzfelbinger and Clemens Heuberger and Daniel Krenn and Helmut Prodinger},
journal= {arXiv preprint arXiv:1611.00258},
year = {2019}
}
Comments
This article supersedes arXiv:1602.04031