Computing a ham-sandwich cut in two dimensions
Journal of Symbolic Computation
Simulation of simplicity: a technique to cope with degenerate cases in geometric algorithms
ACM Transactions on Graphics (TOG)
Bisections and ham-sandwich cuts of convex polygons and polyhedra
Information Processing Letters
On a class of O(n2) problems in computational geometry
Computational Geometry: Theory and Applications
New Lower Bounds for Convex Hull Problems in Odd Dimensions
SIAM Journal on Computing
2-Dimension Ham Sandwich Theorem for Partitioning into Three Convex Pieces
JCDCG '98 Revised Papers from the Japanese Conference on Discrete and Computational Geometry
ISAAC '95 Proceedings of the 6th International Symposium on Algorithms and Computation
STACS '03 Proceedings of the 20th Annual Symposium on Theoretical Aspects of Computer Science
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
Dynamic ham-sandwich cuts in the plane
Computational Geometry: Theory and Applications
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Let R and B be two sets of n points. A ham-sandwich cut is a line that simultaneously bisects R and B, and is known to always exist. This notion can be generalized to the case where each point p ∈ R ∪ B is associated with a weight wp. A ham-sandwich cut can still be proved to exist, even if weights are allowed to be negative. In this paper, we present a O(n log n) algorithm to find a weighted ham-sandwich cut, but we show that deciding whether that cut is unique is 3-SUM hard.