Optimal Polygon Placement

Given a simple polygon P with m vertices and a set S of n points in the plane, we consider the problem of finding a rigid motion placement of P that contains the maximum number of points in S. We present two solutions to this problem that represent time versus space tradeoffs. The first algorithm runs in O(n3 m3 ) expected time using O(n2 m2 ) space. The second algorithm runs in O(n3 m3 log(nm)) deterministic time and O(nm) space. While these algorithms represent a substantial improvement in the time bounds of previous work the main contribution is that the approach is extendible to related rigid motion placement problems including polygonal annulus placement.

• Type: Conference
• Year: 2006
• Where: CCCG
• Authors: Prosenjit Bose, Jason Morrison
• Keywords: Algorithm Runs, CCCG 2006, CCCG 2007, Rigid Motion Placement, Time Versus Space