Maximum Matchings in Geometric Intersection Graphs

Abstract Let G be an intersection graph of n geometric objects in the plane. We show that a maximum matching can found $$O\hspace{0.33325pt}(\rho ^{3\omega /2}n^{\omega /2})$$ O ( ρ 3 ω / 2 n ) time with high probability, where $$\rho $$ is density and $$\omega >2$$ > constant such $$n\times n$$ × matrices multiplied $$O(n^\omega )$$ time. The same result holds for any subgraph , as long representation at hand. For this, we combine algebraic methods, namely computing rank matrix via Gaussian elimination, fact graphs have small separators. also many interesting cases, problem general reduced to case bounded density. In particular, family translates convex object plane $$O(n^{\omega planar disks radii $$[1, \Psi ]$$ [ 1 , Ψ ] $$O\hspace{0.33325pt}(\Psi ^6\log ^{11}\hspace{-0.55542pt}n + ^{12 \omega } n^{\omega 6 log 11 + 12 probability.