LONG NON-CROSSING CONFIGURATIONS IN THE PLANE
نویسندگان
چکیده
منابع مشابه
Long non-crossing configurations in the plane
We revisit several maximization problems for geometric networks design under the non-crossing constraint, first studied by Alon, Rajagopalan and Suri (ACM Symposium on Computational Geometry, 1993). Given a set of n points in the plane in general position (no three points collinear), compute a longest non-crossing configuration composed of straight line segments that is: (a) a matching (b) a Ha...
متن کاملLong non-crossing configurations in the plane (Draft)
It is shown that for any set of 2n points in general position in the plane there is a non-crossing perfect matching of n straight line segments whose total length is at least 2/π of the maximum possible total length of a (possibly crossing) perfect matching on these points. The constant 2/π is best possible and a non-crossing matching whose length is at least as above can be found in polynomial...
متن کاملBottleneck Non-crossing Matching in the Plane
Let P be a set of 2n points in the plane, and letMC (resp.,MNC) denote a bottleneck matching (resp., a bottleneck non-crossing matching) of P . We study the problem of computing MNC. We first prove that the problem is NP-hard and does not admit a PTAS. Then, we present an O(n log n)-time algorithm that computes a noncrossing matching M of P , such that bn(M) ≤ 2 √ 10 · bn(MNC), where bn(M) is t...
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We consider the non-crossing connectors problem, which is stated as follows: Given n simply connected regions R1, . . . , Rn in the plane and finite point sets Pi ⊂ Ri for i = 1, . . . , n, are there non-crossing connectors γi for (Ri, Pi), i.e., arc-connected sets γi with Pi ⊂ γi ⊂ Ri for every i = 1, . . . , n, such that γi ∩ γj = ∅ for all i 6= j? We prove that non-crossing connectors do alw...
متن کاملAnalytic combinatorics of non-crossing configurations
This paper describes a systematic approach to the enumeration of 'non-crossing' geometric configurations built on vertices of a convex n-gon in the plane. It relies on generating functions, symbolic methods, singularity analysis, and singularity perturbation. Consequences are both exact and asymptotic counting results for trees, forests, graphs, connected graphs, dissections, and partitions. Li...
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ژورنال
عنوان ژورنال: Fundamenta Informaticae
سال: 1995
ISSN: 0169-2968
DOI: 10.3233/fi-1995-2245