کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
430572 688045 2013 14 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
All-maximum and all-minimum problems under some measures
موضوعات مرتبط
مهندسی و علوم پایه مهندسی کامپیوتر نظریه محاسباتی و ریاضیات
پیش نمایش صفحه اول مقاله
All-maximum and all-minimum problems under some measures
چکیده انگلیسی

In this paper we investigate the following type of proximity problems: given a set of n   points in the plane P={p1,p2,p3,…,pn}P={p1,p2,p3,…,pn}, for each point pipi find a pair {pj,pk}{pj,pk}, where i≠j≠ki≠j≠k, such that a measure MM defined on the triplet of points {pi,pj,pk}{pi,pj,pk} is maximized or minimized. The cases where MM is the distance from pipi to the segment or line defined by {pj,pk}{pj,pk} have been extensively studied. We study the cases where MM is the sum, product or the difference of the distances from pipi to the points pjpj and pkpk; distance from pipi to the line defined by pjpj and pkpk; the area, perimeter of the triangle defined by pipi, pjpj and pkpk, as well as the radius of the circumcircle defined by them. We also discuss the all-farthest triangle problem in the triangle-distance measure when P is a set of points in 3 dimensions.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Discrete Algorithms - Volume 21, July 2013, Pages 18–31
نویسندگان
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