Computing a ham-sandwich cut in two dimensions
Journal of Symbolic Computation
Triangulating a simple polygon in linear time
Discrete & Computational Geometry
Randomized algorithms
Expected time bounds for selection
Communications of the ACM
2-Dimension Ham Sandwich Theorem for Partitioning into Three Convex Pieces
JCDCG '98 Revised Papers from the Japanese Conference on Discrete and Computational Geometry
Separating point sets in polygonal environments
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
Equitable subdivisions within polygonal regions
Computational Geometry: Theory and Applications - Special issue on the Japan conference on discrete and computational geometry 2004
Line-segment intersection made in-place
Computational Geometry: Theory and Applications
Alternating multiple tributaries + deltas
Proceedings of the 5th workshop on Data management for sensor networks
Dynamic ham-sandwich cuts in the plane
Computational Geometry: Theory and Applications
Equitable subdivisions within polygonal regions
Computational Geometry: Theory and Applications - Special issue on the Japan conference on discrete and computational geometry 2004
JCDCG'04 Proceedings of the 2004 Japanese conference on Discrete and Computational Geometry
Equipartitions of measures by 2-fans
ISAAC'04 Proceedings of the 15th international conference on Algorithms and Computation
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Let P be a simple polygon with m vertices, k of which are reflex, and which contains r red points and b blue points in its interior. Let n=m+r+b. A ham-sandwich geodesic is a shortest path in P between any two points on the boundary of P that simultaneously bisects the red points and the blue points. We present an O (n log k)-time algorithm for finding a ham-sandwich geodesic. We also show that this algorithm is optimal in thealgebraic computation tree model when parameterizing the running time with respect to n and k.