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On Some Proximity Problems of Colored Sets |
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| Authors: | Cheng-Lin Fan Jun Luo Wen-Cheng Wang Fa-Rong Zhong Binhai Zhu |
| Affiliation: | 1. Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences, Shenzhen, 518055, China 2. Huawei Noah’s Ark Laboratory, Shatin, Hong Kong, China 3. State Key Laboratory of Computer Science, Institute of Software, Chinese Academy of Sciences, Beijing, 100190, China 4. College of Mathematics, Physics and Information Technology, Zhejiang Normal University, Jinhua, 321004, China 5. Department of Computer Science, Montana State University, Bozeman, MT, 59717, U.S.A. |
| Abstract: | The maximum diameter color-spanning set problem (MaxDCS) is defined as follows: given n points with m colors, select m points with m distinct colors such that the diameter of the set of chosen points is maximized. In this paper, we design an optimal O(n log n) time algorithm using rotating calipers for MaxDCS in the plane. Our algorithm can also be used to solve the maximum diameter problem of imprecise points modeled as polygons. We also give an optimal algorithm for the all farthest foreign neighbor problem (AFFN) in the plane, and propose algorithms to answer the farthest foreign neighbor query (FFNQ) of colored sets in two- and three-dimensional space. Furthermore, we study the problem of computing the closest pair of color-spanning set (CPCS) in d-dimensional space, and remove the log m factor in the best known time bound if d is a constant. |
| Keywords: | computational geometry colored set algorithm maximum diameter color-spanning set problem |
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