Computational geometry: an introduction
Computational geometry: an introduction
Computing
An optimal algorithm for finding minimal enclosing triangles
Journal of Algorithms
New upper bounds in Klee's measure problem
SIAM Journal on Computing
Computing the smallest k-enclosing circle and related problems
Computational Geometry: Theory and Applications
Map labeling heuristics: provably good and practically useful
Proceedings of the eleventh annual symposium on Computational geometry
Computational geometry: algorithms and applications
Computational geometry: algorithms and applications
Translating a convex polygon to contain a maximum number of points
Computational Geometry: Theory and Applications
Data collection for the Sloan Digital Sky Survey—a network-flow heuristic
Proceedings of the seventh annual ACM-SIAM symposium on Discrete algorithms
Static and Dynamic Algorithms for k-Point Clustering Problems
WADS '93 Proceedings of the Third Workshop on Algorithms and Data Structures
Offset-Polygon Annulus Placement Problems
WADS '97 Proceedings of the 5th International Workshop on Algorithms and Data Structures
Maximizing the overlap of two planar convex sets under rigid motions
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
Covering points with a polygon
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
Maximizing the overlap of two planar convex sets under rigid motions
Computational Geometry: Theory and Applications
Covering points with a polygon
Computational Geometry: Theory and Applications
Largest empty circle centered on a query line
Journal of Discrete Algorithms
Offset polygon and annulus placement problems
Computational Geometry: Theory and Applications
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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 (allowing both translation and rotation) that contains the maximum number of points in S. We present first an algorithm requiring O(n^2km^2log(mn)) time and O(n + m) space, where k is the maximum number of points contained. We then give a refinement that makes use of bucketing to improve the running time to O(nk^2c^2m^2log(mk)), where c is the ratio of length to width of the polygon. This provides an improvement over the best previously known algorithm linear in n when k is large (@Q(n)) and a cubic when k is small. We also show that the algorithm can be extended to solve bichromatic and general weighted variants of the problem. The algorithm is self-contained and utilizes the geometric properties of the containing regions in the parameter space of transformations.