2014/09/25 by Sariel Har-Peled, Har-Peled, Sariel, Banjamin Raichel +1
Computer Science · Engineering · #Automated Road and Building Extraction #Computational Geometry (cs.CG) #Computational Geometry and Mesh Generation #Data Management and Algorithms #FOS: Computer and information sciences
paper · pdf · doi:10.48550/arxiv.1409.7425
openalex publication_date 2014/09/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
We provide a general framework for getting expected linear time constant factor approximations (and in many cases FPTASs) to several well-known problems in Computational Geometry, such as k-center clustering and farthest nearest neighbor. The new approach is robust to variations in the input problem, and yet it is simple, elegant, and practical. In particular, many of these well-studied problems, which fit easily into our framework, either previously had no linear time approximation algorithm, or required rather involved algorithms and analysis. A short list of the problems we consider includes farthest nearest neighbor, k-center clustering, smallest disk enclosing k points, Hausdorff distance, kth largest distance, kth smallest m-nearest neighbor distance, kth heaviest edge in the MST, and other spanning-forest type problems, problems involving upward closed set systems, and more. Finally, we show how to extend our framework such that the linear running time bound holds with high probability.