20.500.12556/DiRROS-18632 Maximum matchings in geometric intersection graphs Let $G$ be an intersection graph of $n$ geometric objects in the plane. We show that a maximum matching in $G$ can be found in $O(\rho^{3\omega/2}n^{\omega/2})$ time with high probability, where $\rho$ is the density of the geometric objects and $\omega>2$ is a constant such that $n \times n$ matrices can be multiplied in $O(n^\omega)$ time. The same result holds for any subgraph of $G$, as long as a geometric representation is at hand. For this, we combine algebraic methods, namely computing the rank of a matrix via Gaussian elimination, with the fact that geometric intersection graphs have small separators. We also show that in many interesting cases, the maximum matching problem in a general geometric intersection graph can be reduced to the case of bounded density. In particular, a maximum matching in the intersection graph of any family of translates of a convex object in the plane can be found in $O(n^{\omega/2})$ time with high probability, and a maximum matching in the intersection graph of a family of planar disks with radii in $[1, \Psi]$ can be found in $O(\Psi^6\log^{11} n + \Psi^{12 \omega} n^{\omega/2})$ time with high probability. computational geometry geometric intersection graphs disk graphs unit-disk graphs matchings true false true Angleški jezik Ni določen Neznano 2024-04-08 12:06:44 2024-04-08 12:06:44 2024-04-09 03:40:10 0000-00-00 00:00:00 2023 0 0 str. 550-579 iss. 3 Vol. 70 Oct. 2023 0000-00-00 Zaloznikova Objavljeno NiDoloceno 0000-00-00 0000-00-00 2023-10-01 004.42:515.17 0179-5376 10.1007/s00454-023-00564-3 163998979 s00454-023-00564-3-1.pdf s00454-023-00564-3-1.pdf 1 CFA5DBABF17761B11ACC25F11DBAF784 df7c7eecceef3072688cd36aeb020874fd36e88bacdfcc5008030b30216cd9ff 5a05ccab-f580-11ee-ae20-001a4af901a5 https://dirros.openscience.si/Dokument.php?lang=slv&id=25436 https://link.springer.com/article/10.1007/s00454-023-00564-3 1 f12ea699-f57e-11ee-ae20-001a4af901a5 https://dirros.openscience.si/Dokument.php?lang=slv&id=25435 Inštitut za matematiko, fiziko in mehaniko 0 0 0