On Isolating Points Using Disks

TL;DR

This paper addresses the problem of selecting a minimal set of disks to block all paths between points in a plane, providing a polynomial-time approximation algorithm and pioneering this specific optimization challenge.

Contribution

First to study the problem of isolating points with disks, offering a constant factor approximation algorithm in polynomial time.

Findings

A greedy algorithm achieves a constant factor approximation.

The problem is computationally tractable with polynomial algorithms.

This is the first study of the disk-based point isolation optimization.

Abstract

In this paper, we consider the problem of choosing disks (that we can think of as corresponding to wireless sensors) so that given a set of input points in the plane, there exists no path between any pair of these points that is not intercepted by some disk. We try to achieve this separation using a minimum number of a given set of unit disks. We show that a constant factor approximation to this problem can be found in polynomial time using a greedy algorithm. To the best of our knowledge we are the first to study this optimization problem.