On Some Proximity Problems of Colored Sets  

作　　者：范成林 罗军 王文成 钟发荣 朱滨海 

机构地区：[1]Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences [2]Huawei Noah's Ark Laboratory [3]State Key Laboratory of Computer Science, Institute of Software, Chinese Academy of Sciences [4]College of Mathematics, Physics and Information Technology, Zhejiang Normal University [5]Department of Computer Science, Montana State University,Bozeman, MT 59717, U.S.A. Member,ACM

出　　处：《Journal of Computer Science & Technology》2014年第5期879-886,共8页计算机科学技术学报（英文版）

基　　金：supported by the International Science and Technology Cooperation Program of China under Grant No.2010DFA92720;the National Natural Science Foundation of China under Grant Nos.11271351,60928006,and 61379087

摘　　要：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.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.

关 键 词：computational geometry colored set algorithm maximum diameter color-spanning set problem 

分 类 号：TP301.6[自动化与计算机技术—计算机系统结构] TU472[自动化与计算机技术—计算机科学与技术]