SIAM Journal on Computing
Topologically sweeping an arrangement
STOC '86 Proceedings of the eighteenth annual ACM symposium on Theory of computing
Constructing arrangements of lines and hyperplanes with applications
SIAM Journal on Computing
Searching for empty convex polygons
SCG '88 Proceedings of the fourth annual symposium on Computational geometry
Fining k points with minimum spanning trees and related problems
SCG '89 Proceedings of the fifth annual symposium on Computational geometry
Discrete & Computational Geometry
Computing the largest empty convex subset of a set of points
SCG '85 Proceedings of the first annual symposium on Computational geometry
Iterated nearest neighbors and finding minimal polytypes
SODA '93 Proceedings of the fourth annual ACM-SIAM Symposium on Discrete algorithms
Finding subsets maximizing minimum structures
Proceedings of the sixth annual ACM-SIAM symposium on Discrete algorithms
SODA '94 Proceedings of the fifth annual ACM-SIAM symposium on Discrete algorithms
An annotated bibliography of combinatorial optimization problems with fixed cardinality constraints
Discrete Applied Mathematics - Special issue: 2nd cologne/twente workshop on graphs and combinatorial optimization (CTW 2003)
Algorithms for optimal outlier removal
Journal of Discrete Algorithms
An annotated bibliography of combinatorial optimization problems with fixed cardinality constraints
Discrete Applied Mathematics - Special issue: 2nd cologne/twente workshop on graphs and combinatorial optimization (CTW 2003)
Finding minimum area simple pentagons
Operations Research Letters
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Given a set P ofn points in the plane, we wish tofind a set Q ⊂ P ofk points for which the convex hullconv(Q has the minimum area. Wesolve this, and the related problem of finding a minimum area convexk-gon, in timeO(n2log n) for fixedk, almost matching known bounds forthe minimum area triangle problem. Our algorithm is based on finding acertain number of nearest verticalneighbors to each line segment determined by two inputpoints. We use a classical result of Ramsey theory to prove that thesenearest neighbors suffice to determine the minimum convexk-gon.