SIAM Journal on Computing
Combinatorial algorithms for integrated circuit layout
Combinatorial algorithms for integrated circuit layout
Long non-crossing configurations in the plane
SCG '93 Proceedings of the ninth annual symposium on Computational geometry
Vertical Decomposition of Shallow Levels in 3-Dimensional Arrangements and Its Applications
SIAM Journal on Computing
Computing Euclidean bottleneck matchings in higher dimensions
Information Processing Letters
Reductions among high dimensional proximity problems
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
A Divide-and-Conquer Algorithm for Min-Cost Perfect Matching in the Plane
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
Computing the visibility graph of points within a polygon
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
Compatible geometric matchings
Computational Geometry: Theory and Applications
Non-crossing matchings of points with geometric objects
Computational Geometry: Theory and Applications
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Let P be a set of 2n points in the plane, and let M"C (resp., M"N"C) denote a bottleneck matching (resp., a bottleneck non-crossing matching) of P. We study the problem of computing M"N"C. We first prove that the problem is NP-hard and does not admit a PTAS. Then, we present an O(n^1^.^5log^0^.^5n)-time algorithm that computes a non-crossing matching M of P, such that bn(M)=