Faster Approximation for Maximum Independent Set on Unit Disk Graph

TL;DR

This paper presents a faster approximation algorithm for the maximum independent set problem on unit disk graphs, reducing the time complexity from O(n^2 log n) to O(n^2) while maintaining a factor 2 approximation.

Contribution

It introduces an O(n^2) time and space algorithm for a factor 2 approximation, improving over previous methods that required O(n^2 log n) time.

Findings

Achieves a factor 2 approximation in O(n^2) time

Reduces computational complexity compared to prior algorithms

Provides a practical approach for large datasets

Abstract

Maximum independent set from a given set $D$ of unit disks intersecting a horizontal line can be solved in $O(n^2)$ time and $O(n^2)$ space. As a corollary, we design a factor 2 approximation algorithm for the maximum independent set problem on unit disk graph which takes both time and space of $O(n^2)$. The best known factor 2 approximation algorithm for this problem runs in $O(n^2 \log n)$ time and takes $O(n^2)$ space [Jallu and Das 2016, Das et al. 2016].