How to Sort in a Refrigerator: Simple Entropy-Sensitive Strictly In-Place Sorting Algorithms

TL;DR

This paper introduces simple, entropy-sensitive in-place sorting algorithms suitable for memory-limited embedded systems, achieving optimal runtime based on input entropy.

Contribution

It presents the first comparison-based, strictly in-place sorting algorithms with optimal entropy-based runtime, using novel stack-based natural mergesort paradigms.

Findings

Algorithms are strictly in-place with O(1) extra memory.

Runtime is optimal in terms of input entropy H(A).

Algorithms are simple and practical for embedded systems.

Abstract

While modern general-purpose computing systems have ample amounts of memory, it is still the case that embedded computer systems, such as in a refrigerator, are memory limited; hence, such embedded systems motivate the need for strictly in-place algorithms, which use only O(1) additional memory besides that used for the input. In this paper, we provide the first comparison-based sorting algorithms that are strictly in-place and have a running time that is optimal in terms of the run-based entropy, H(A), of an input array, A, of size n. In particular, we describe two remarkably simple paradigms for implementing stack-based natural mergesort algorithms to be strictly in-place in O(n(1 + H(A))) time.