We present a (1−ε)-approximation algorithms for maximum cardinality matchings in disk intersection graphs -- all with near linear running time. We also present estimation algorithm that returns (1±ε)-approximation to the size of such matchings -- this algorithms run in linear time for unit disks, and O(nlogn) for general disks (as long as the density is relatively small).
@article{arxiv.2201.01849,
title = {Approximation Algorithms for Maximum Matchings in Geometric Intersection Graphs},
author = {Sariel Har-Peled and Everett Yang},
journal= {arXiv preprint arXiv:2201.01849},
year = {2022}
}