Bottleneck non-crossing matching in the plane

Abu-Affash, A. Karim; Carmi, Paz; Katz, Matthew J.; Trabelsi, Yohai

doi:10.1016/j.comgeo.2013.10.005

Cited by 14 publications

(2 citation statements)

References 21 publications

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“…It is known, for example, that it is NP-hard to find a maximum noncrossing matching in certain geometric graph [3]. The problem of, given an even number of points, finding a noncrossing matching that minimizes the length of the longest edge is also known to be NP-hard [2].…”

Section: Covering Trees Versus Perfect Rainbow Polygonsmentioning

confidence: 99%

Rainbow polygons for colored point sets in the plane

Flores-Peñaloza¹,

Kanō²,

Martínez-Sandoval³

et al. 2020

Preprint

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Given a colored point set in the plane, a perfect rainbow polygon is a simple polygon that contains exactly one point of each color, either in its interior or on its boundary. Let rb-index(S) denote the smallest size of a perfect rainbow polygon for a colored point set S, and let rb-index(k) be the maximum of rb-index(S) over all k-colored point sets in general position; that is, every k-colored point set S has a perfect rainbow polygon with at most rb-index(k) vertices. In this paper, we determine the values of rb-index(k) up to k = 7, which is the first case where rb-index(k) = k, and we prove that for k ≥ 5,Furthermore, for a k-colored set of n points in the plane in general position, a perfect rainbow polygon with at most 10 k 7 + 11 vertices can be computed in O(n log n) time. * A preliminary version was presented at the 18th Spanish Meeting on Computational Geometry (2019).

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Section: Covering Trees Versus Perfect Rainbow Polygonsmentioning

confidence: 99%

Rainbow polygons for colored point sets in the plane

Flores-Peñaloza¹,

Kanō²,

Martínez-Sandoval³

et al. 2020

Preprint

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“…A perfect matching M of P is a perfect matching in the complete Euclidean graph induced by P. Let bn(M) denote the length of a longest edge of M. A bottleneck matching MC of P is a perfect matching of P that mmlmlzes bn(-).In computational geometry, [3] Bottleneck matching may be of two types namely bottleneck crossing and bottleneck non crossing matching. [4] A non-crossing matching of P is a perfect matching whose edges are pairwise disjoint. In this paper ,we study the problem of computing a bottleneck non crossing matching of P that is , a non crossing matching MNC of P that minimizes bn(-) in a set of convex points.…”

Section: Iintroductionmentioning

confidence: 99%

Implementation of bottleneck non cross matching for a set of convex points using convex hull and development of an image search algorithim

Sarkar

Gupta

2014

2014 International Conference on High Performance Computing and Applications (ICHPCA)

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The convex hull of a set X of points in the Euclidean plane is the smallest convex set that contains X. Let P be a set of 2n points in the plane which are in convex position. In this paper we propose to compute in o (n 3 ) time and 0(n 2 ) space a bottleneck non-crossing matching of P. We compute the longest edge of bottleneck matching via dynamic programming. We extend our idea towards several applications of convex hull which includes Pattern matching and shape based image retrieval .The results shown in this paper illustrate the various applications of convex hull especially on shape based image retrieval and implements the bottleneck non cross matching on a set of convex points in 0 (n 3 ) time and 0(n 2 ) space.

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