Optimal placement of convex polygons to maximize point containment
- Middlebury College, VT (United States)
- Cornell Univ., Ithaca, NY (United States)
Given a convex polygon P with m vertices and a set S of n points in the plane, we consider the problem of finding a placement of P that contains the maximum number of points in S. We allow both translation and rotation. Our algorithm is self-contained and utilizes the geometric properties of the containing regions in the parameter space of transformations. The algorithm requires O(nk{sup 2} m{sup 2} log(mk)) time and O(n + m) space, where k is the maximum number of points contained. This provides a linear improvement over the best previously known algorithm when k is large ({Theta}(n)) and a cubic improvement when k is small. We also show that the algorithm can be extended to solve bichromatic and general weighted variants of the problem.
- OSTI ID:
- 416792
- Report Number(s):
- CONF-960121--
- Country of Publication:
- United States
- Language:
- English
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