On Some Proximity Problems of Colored Sets

• DOI: 10.1007/s11390-014-1475-0
• Publication Date: 2014-09-21T09:42:35Z
• Authors: Cheng-Lin Fan; Jun Luo; Wen-Cheng Wang; Fa-Rong Zhong; Binhai Zhu
• Keywords: Colored; Theory of computation; Constant (computer programming); Computational Geometry

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 logn) time algorithm using rotating calipers for MaxDCS problem 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 factor logm of the best known time bound if we treat d as a constant.