Hougardy, StefanStefanHougardyTammemaa, KarolinaKarolinaTammemaa2026-05-042026-05-042026-06-01Theory of Computing Systems 70 (2): 25 (2026)https://hdl.handle.net/11420/62869We study the Euclidean minimum weight perfect matching problem for n points in the plane. It is known that any deterministic approximation algorithm whose approximation ratio depends only on n requires at least Ω(nlogn) time. We propose such an algorithm for the Euclidean minimum weight perfect matching problem with runtime O(nlogn) and show that it has approximation ratio O(n0.206). This improves the so far best known approximation ratio of n/2. We also develop an O(nlogn) algorithm for the Euclidean minimum weight perfect matching problem in higher dimensions and show it has approximation ratio O(n0.412) in all fixed dimensions.en1433-049020262Springerhttps://creativecommons.org/licenses/by/4.0/Approximation algorithmsEuclidean matchingNatural Sciences and Mathematics::510: MathematicsJournal Articlehttps://doi.org/10.15480/882.1702810.1007/s00224-025-10254-710.15480/882.17028