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:
“... it seems to have been my luck to stumble into various forms of progress, to which I have been of the smallest possible use; yet for whose sake I have suffered the discomfort attending all action in moral improvements, without the happiness of knowing that this was clearly quite worth while.”
—Elizabeth Stuart Phelps (1844–1911)
“It is a good lesson—though it may often be a hard one—for a man who has dreamed of literary fame, and of making for himself a rank among the world’s dignitaries by such means, to step aside out of the narrow circle in which his claims are recognized, and to find how utterly devoid of all significance, beyond that circle, is all that he achieves, and all he aims at.”
—Nathaniel Hawthorne (1804–1864)
“I tell you, sir, the only safeguard of order and discipline in the modern world is a standardized worker with interchangeable parts. That would solve the entire problem of management.”
—Jean Giraudoux (1882–1944)