Recursive Sorting in Lattices

TL;DR

This paper introduces a recursive method for sorting sequences in distributive lattices, reducing complexity from exponential to quadratic, inspired by Pascal's triangle, and generalizing insertion sort for lattices.

Contribution

It presents the first practical recursive algorithm for sorting in distributive lattices with quadratic complexity, improving over previous exponential methods.

Findings

Quadratic complexity algorithm for lattice sorting

Generalizes insertion sort to lattice structures

Practical recursive approach for distributive lattices

Abstract

The direct application of the definition of sorting in lattices is impractical because it leads to an algorithm with exponential complexity. In this paper we present for distributive lattices a recursive formulation to compute the sort of a sequence. This alternative formulation is inspired by the identity that underlies Pascal's triangle. It provides quadratic complexity and is in fact a generalization of insertion sort for lattices.