Approximation Algorithms for Maximum Matchings in Geometric Intersection Graphs

TL;DR

This paper introduces near-linear time approximation algorithms for maximum matchings in disk intersection graphs, providing efficient solutions for both general and unit disks with high accuracy.

Contribution

It develops $(1- \varepsilon)$-approximation algorithms and estimation algorithms with linear or near-linear running times for maximum matchings in disk intersection graphs.

Findings

Achieves near-linear time algorithms for maximum matchings.

Provides estimation algorithms with $(1\pm \varepsilon)$ accuracy.

Effective for both unit and general disks with low density.

Abstract

We present a $(1- \varepsilon)$-approximation algorithms for maximum cardinality matchings in disk intersection graphs -- all with near linear running time. We also present estimation algorithm that returns $(1\pm \varepsilon)$-approximation to the size of such matchings -- this algorithms run in linear time for unit disks, and $O(n \log n)$ for general disks (as long as the density is relatively small).