Covering and Piercing Disks with Two Centers

TL;DR

This paper investigates algorithms for covering and piercing a set of disks in the plane with two congruent disks, providing exact and approximation solutions for these geometric problems.

Contribution

It introduces new algorithms for the two-center problems involving disks, addressing both piercing and covering cases with exact and approximate methods.

Findings

Developed exact algorithms for the piercing problem.

Designed approximation algorithms for the covering problem.

Analyzed the complexity and efficiency of the proposed algorithms.

Abstract

We give exact and approximation algorithms for two-center problems when the input is a set $\mathcal{D}$ of disks in the plane. We first study the problem of finding two smallest congruent disks such that each disk in $\mathcal{D}$ intersects one of these two disks. Then we study the problem of covering the set $\mathcal{D}$ by two smallest congruent disks.