Faster Bottleneck Non-crossing Matchings of Points in Convex Position

TL;DR

This paper introduces a quadratic-time algorithm for finding bottleneck non-crossing matchings among points in convex position, significantly improving the previous cubic-time solutions.

Contribution

It presents the first quadratic-time algorithm for bottleneck non-crossing matchings in convex position, enhancing computational efficiency.

Findings

Quadratic-time algorithm for convex position points

Improved from previous cubic-time algorithms

Efficiently finds bottleneck non-crossing matchings

Abstract

Given an even number of points in a plane, we are interested in matching all the points by straight line segments so that the segments do not cross. Bottleneck matching is a matching that minimizes the length of the longest segment. For points in convex position, we present a quadratic-time algorithm for finding a bottleneck non-crossing matching, improving upon the best previously known algorithm of cubic time complexity.