Minimal Enclosing Circle and Two and Three Point Partition of a Plane

Partitions of a plane, based on two or three of its points, are introduced. The study of these partitions is applied to finding the minimal enclosing circle (MEC) for a set S of n planar points. MEC(S), the MEC of n points of S, is defined by either a pair of S points with the largest distance (tight two-tuple) or by a triplet of S points spread on more than half of its circumference (tight three-tuple) with the largest radius. An extension for an existing MEC by an outside point PS is a MEC for point P and the points of the tight tuple for the existing MEC. It has a larger radius than existing MEC. The MEC problem is dual to a problem of finding an optimal partition of S-plane by two or three points of S defined with the largest circular region. A two point partition divides the S-plane in 4 regions, a three point

• Type: Conference
• Year: 2006
• Where: CSC
• Authors: Felix Friedman
• Keywords: CSC 2006, CSC 2007, Minimal Enclosing Circle, Point Partition, Tight Tuple