Towards universally optimal sorting algorithms

TL;DR

This paper introduces a new paradigm for assessing the optimality of algorithms based on problem-dependent parameters, leading to the development of a novel sorting algorithm and a promising framework for future research.

Contribution

It formalizes a generalized optimality paradigm incorporating implicit parameters and presents a new measure of sortedness with an optimal partition sort algorithm.

Findings

Revisits existing sorting algorithms under the new paradigm

Introduces a novel measure of sortedness

Proposes an optimal algorithm based on partition sort

Abstract

We formalize a new paradigm for optimality of algorithms, that generalizes worst-case optimality based only on input-size to problem-dependent parameters including implicit ones. We re-visit some existing sorting algorithms from this perspective, and also present a novel measure of sortedness that leads to an optimal algorithm based on partition sort. This paradigm of measuring efficiency of algorithms looks promising for further interesting applications beyond the existing ones.