Optimal Point Set Partitioning using Rigid Motion Star Placement

We consider the problem of determining the placement of a star R on a set P of n points in the plane such that a given objective function is maximized. A star R is a set of m rays {r1, . . . , rm} in R2 , emanating from a point p such that the angle between two consecutive rays is 2π m . A cone defined by two consecutive rays is c-occupied if it contains at least c points of P. Our main result is an O(n3 m2 ) expected time (and O(n3 m2 log nm) deterministic time) algorithm to find the rigid motion placement of R that maximizes the number of c-occupied cones. We then show how this technique can be extended to solve several other optimization problems.

• Type: Conference
• Year: 2007
• Where: CCCG
• Authors: Prosenjit Bose, Jason Morrison
• Keywords: CCCG 2007, Computational Geometry, Consecutive Rays, Objective Function, Rigid Motion Placement