Smallest Circle Problem
The smallest-circle problem or minimum covering circle problem is a mathematical problem of computing the smallest circle that contains all of a given set of points in the Euclidean plane. The corresponding problem in n-dimensional space, the smallest bounding-sphere problem, is to compute the smallest n-sphere that contains all of a given set of points. The smallest-circle problem was initially proposed by the English mathematician James Joseph Sylvester in 1857.
The smallest-circle problem in the plane is an example of a facility location problem in which the location of a new facility must be chosen to provide service to a number of customers, minimizing the farthest distance that any customer must travel to reach the new facility. Both the smallest circle problem in the plane, and the smallest bounding sphere problem in any higher-dimensional space of bounded dimension, may be solved in linear time.
Read more about Smallest Circle Problem: Characterization, Linear-time Solutions, Other Algorithms, Weighted Variants of The Problem
Famous quotes containing the words smallest, circle and/or problem:
“... for the poor the whole world is a self-constituted critic; your smallest action is open to debate.”
—Alice Foote MacDougall, U.S. businesswoman. (1867-1945)
“The passion of love is essentially selfish, while motherhood widens the circle of our feelings.”
—HonorĂ© De Balzac (17991850)
“And just as there are no words for the surface, that is,
No words to say what it really is, that it is not
Superficial but a visible core, then there is
No way out of the problem of pathos vs. experience.”
—John Ashbery (b. 1927)