Cyclic space-filling curves and their clustering property

TL;DR

This paper introduces a new family of cyclic space-filling curves that outperform or match the Hilbert curve in clustering, with simpler construction and faster evaluation, applicable across all dimensions.

Contribution

It presents a novel construction algorithm for cyclic space-filling curves, including H-curves, with improved simplicity and efficiency over existing curves like the Hilbert curve.

Findings

The new curves have clustering properties comparable or superior to the Hilbert curve.

Construction of the curves is simpler and evaluation is significantly faster.

The approach is applicable in all dimensions.

Abstract

In this paper we introduce an algorithm of construction of cyclic space-filling curves. One particular construction provides a family of space-filling curves in all dimensions (H-curves). They are compared here with the Hilbert curve in the sense of clustering properties, and it turns out that the constructed curve is very close and sometimes a bit better than the Hilbert curve. At the same time, its construction is more simple and evaluation is significantly faster.