Emerge-Sort: Converging to Ordered Sequences by Simple Local Operators

TL;DR

Emerge-Sort is a self-organizing sorting algorithm that uses simple local operators to converge to sorted sequences without prior knowledge of sorting order, demonstrating an O(n^2) runtime.

Contribution

The paper introduces Emerge-Sort, a novel self-organizing sorting method based on local operators, validated through experiments showing its convergence properties.

Findings

Emerge-Sort converges to sorted sequences using local comparison and swap operators.

The algorithm exhibits an O(n^2) runtime behavior.

It demonstrates a trade-off with classical algorithms, with an n/logn delay coefficient.

Abstract

In this paper we examine sorting on the assumption that we do not know in advance which way to sort a sequence of numbers and we set at work simple local comparison and swap operators whose repeating application ends up in sorted sequences. These are the basic elements of Emerge-Sort, our approach to self-organizing sorting, which we then validate experimentally across a range of samples. Observing an O(n2) run-time behaviour, we note that the n/logn delay coefficient that differentiates Emerge-Sort from the classical comparison based algorithms is an instantiation of the price of anarchy we pay for not imposing a sorting order and for letting that order emerge through the local interactions.