Bottleneck Matching in the Plane

TL;DR

This paper introduces an efficient algorithm for computing bottleneck matchings in planar point sets, leveraging advanced matrix multiplication techniques to improve computational complexity.

Contribution

It presents a novel deterministic algorithm with improved runtime for bottleneck matching in the plane, utilizing matrix multiplication exponent.

Findings

Algorithm runs in O(n^{ω/2} log n) time

Uses matrix multiplication to optimize matching computation

Achieves faster performance compared to previous methods

Abstract

We present an algorithm for computing a bottleneck matching in a set of $n=2\ell$ points in the plane, which runs in $O(n^{\omega/2}\log n)$ deterministic time, where $\omega\approx 2.37$ is the exponent of matrix multiplication.