Congruence Testing of Point Sets in 4 Dimensions

TL;DR

This paper presents an efficient algorithm for testing congruence of point sets in four-dimensional space, utilizing advanced geometric concepts and achieving a time complexity of O(n log n).

Contribution

It introduces a novel O(n log n) algorithm for 4D point set congruence testing and revisits key geometric structures relevant to the problem.

Findings

Congruence testing in 4D can be performed efficiently in O(n log n) time.

Revisiting 4D geometry concepts aids in developing the congruence testing algorithm.

The approach leverages angles, distances, Hopf fibrations, and Coxeter groups to solve the problem.

Abstract

Congruence between two n-point sets in 4 dimension can be checked in O(n log n) time. On the way to establishing this result, we revisit several parts of 4-dimensional geometry, such as angles and distances between planes, Hopf fibrations, and Coxeter groups.