Geometric Algorithms for Minimal Enclosing Discs in Strictly Convex Normed Planes

TL;DR

This paper extends classical minimal enclosing disk algorithms to strictly convex normed planes, demonstrating their validity in this broader geometric setting and building on prior work on circumcenter locations.

Contribution

It proves the validity of Elzinga--Hearn and Shamos--Hoey algorithms for minimal enclosing disks in strictly convex normed planes, expanding their applicability.

Findings

Algorithms are valid in strictly convex normed planes.

Builds on prior geometric background by Alonso, Martini, and Spirova.

Extends classical Euclidean algorithms to a broader geometric context.

Abstract

With the geometric background provided by Alonso, Martini, and Spirova on the location of circumcenters of triangles in normed planes, we show the validity of the Elzinga--Hearn algorithm and the Shamos--Hoey algorithm for solving the minimal enclosing disk problem in strictly convex normed planes.