10.1007/bf01758842 doi Given a set of pointsV in the plane, the Euclidean bottleneck matching problem is to match each point with some other point such that the longest Euclidean distance between matched points, resulting from this matching, is minimized. To solve this problem, we definek-relative neighborhood graphs, (kRNG) which are derived from Toussaint's relative neighborhood graphs (RNG). Two points are calledk-relative neighbors if and only if there are less thank points ofV which are closer to both of the two points than the two points are to each other. AkRNG is an undirected graph (V,Erk) whereErk is the set of pairs of points ofV which arek-relative neighbors. We prove that there exists an optimal solution of the Euclidean bottleneck matching problem which is a subset ofEr17. We also prove that ¦Erk¦ < 18kn wheren is the number of points in setV. Our algorithm would construct a 17RNG first. This takesO(n2) time. We then use Gabow and Tarjan's bottleneck maximum cardinality matching algorithm for general graphs whose time-complexity isO((n logn)0.5m), wherem is the number of edges in the graph, to solve the bottleneck maximum cardinality matching problem in the 17RNG. This takesO(n1.5 log0.5n) time. The total time-complexity of our algorithm for the Euclidean bottleneck matching problem isO(n2 +n1.5 log0.5n). https://scigraph.springernature.com/explorer/license/ articles 1992-12 177-194 Solving the Euclidean bottleneck matching problem byk-relative neighborhood graphs http://link.springer.com/10.1007/BF01758842 false 1992-12-01 2019-04-11T09:53 research_article en Chang M. S. C. Y. Tang National Tsing Hua University Institute of Computer Science, National Tsing Hua University, 30043, Hsinchu, Taiwan, Republic of China pub.1036591041 dimensions_id 0178-4617 Algorithmica 1432-0541 Academia Sinica Academia Sinica, Taipei, Taiwan, Republic of China National Tsing Hua University, Hsinchu, Taiwan 1-6 R. C. T. Lee Institute of Computer Science and Information Engineering, National Chung Cheng University, 62107, Chiayi, Taiwan, Republic of China National Chung Cheng University Computation Theory and Mathematics 8 readcube_id ae4e49e1e25feb22f7a424ca25759580a5617d1da5b4f54ef40738c43f634130 Springer Nature - SN SciGraph project Information and Computing Sciences