Approximation Algorithms for Maximum Matchings in Geometric Intersection Graphs

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).