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
Compatible geometric matchings
Computational Geometry: Theory and Applications
LATIN'10 Proceedings of the 9th Latin American conference on Theoretical Informatics
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Let P be a set of 2n points in the plane, and let MC (resp., MNC) denote a bottleneck matching (resp., a bottleneck non-crossing matching) of P. We study the problem of computing MNC. We present an O(n1.5log0.5n)-time algorithm that computes a non-crossing matching M of P, such that $bn(M) \le 2\sqrt{10} \cdot bn(M_{\rm NC})$, where bn(M) is the length of a longest edge in M. An interesting implication of our construction is that $bn(M_{\rm NC})/bn(M_{\rm C}) \le 2\sqrt{10}$. We also show that when the points of P are in convex position, one can compute MNC in O(n3) time. (In the full version of this paper, we also prove that the problem is NP-hard and does not admit a PTAS.)