Minimum Enclosing Circle with Few Extra Variables
نویسندگان
چکیده
Asano et al. [JoCG 2011] proposed an open problem of computing the minimum enclosing circle of a set of n points in R2 given in a read-only array in sub-quadratic time. We show that Megiddo’s prune and search algorithm for computing the minimum radius circle enclosing the given points can be tailored to work in a read-only environment in O(n1+ ) time using O(logn) extra space, where is a positive constant less than 1. As a warm-up, we first solve the same problem in an in-place setup in linear time with O(1) extra space. 1998 ACM Subject Classification F.2.2 Nonnumerical Algorithms and Problems
منابع مشابه
Prune-and-search with limited workspace
Prune-and-search is an excellent algorithmic paradigm for solving various optimization problems. We provide a general scheme for prune-and-search technique and show how to implement it in space-efficient manner. We consider both the in-place and read-only model which have several advantages compared to the traditional model of computation. Our technique can be applied to a large number of probl...
متن کاملSolution Methodologies for the Smallest Enclosing Circle Problem
Given a set of circles C = {c1, ..., cn} on the Euclidean plane with centers {(a1, b1), ..., (an, bn)} and radii {r1, ..., rn}, the smallest enclosing circle (of fixed circles ) problem is to find the circle of minimum radius that encloses all circles in C. We survey four known approaches for this problem, including a second order cone reformulation, a subgradient approach, a quadratic programm...
متن کاملIdentification and Elimination of Interior Points for the Minimum Enclosing Ball Problem
Given A := {a, . . . , am} ⊂ Rn, we consider the problem of reducing the input set for the computation of the minimum enclosing ball of A. In this note, given an approximate solution to the minimum enclosing ball problem, we propose a simple procedure to identify and eliminate points in A that are guaranteed to lie in the interior of the minimum-radius ball enclosing A. Our computational result...
متن کاملMinimum Enclosing Circle of a Set of Static Points with Dynamic Weight from One Free Point
Given a set S of n static points and a free point p in the Euclidean plane, we study a new variation of the minimum enclosing circle problem, in which a dynamic weight that equals to the reciprocal of the distance from the free point p to the undetermined circle center is included. In this work, we prove the optimal solution of the new problem is unique and lies on the boundary of the farthest-...
متن کاملDisk Constrained 1-Center Queries
We show that a set P of n points in the plane can be preprocessed in O(n log n)-time to construct a data structure supporting O(log n)-time queries of the following form: Find the minimum enclosing circle of P with center on a given disk.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2012