An Extended Note on the Comparison-optimal Dual Pivot Quickselect
Combinatorics
2016-10-18 v2 Data Structures and Algorithms
Abstract
In this note the precise minimum number of key comparisons any dual-pivot quickselect algorithm (without sampling) needs on average is determined. The result is in the form of exact as well as asymptotic formul\ae{} of this number of a comparison-optimal algorithm. It turns out that the main terms of these asymptotic expansions coincide with the main terms of the corresponding analysis of the classical quickselect, but still---as this was shown for Yaroslavskiy quickselect---more comparisons are needed in the dual-pivot variant. The results are obtained by solving a second order differential equation for the generating function obtained from a recursive approach.
Cite
@article{arxiv.1607.05008,
title = {An Extended Note on the Comparison-optimal Dual Pivot Quickselect},
author = {Daniel Krenn},
journal= {arXiv preprint arXiv:1607.05008},
year = {2016}
}