Bottleneck non-crossing matching in the plane

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

doi:10.1016/j.comgeo.2013.10.005

Bottleneck non-crossing matching in the plane

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

Department of Computer Science

Research output: Contribution to journal › Article › peer-review

18 Scopus citations

Abstract

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 first prove that the problem is NP-hard and does not admit a PTAS. Then, we present an O(^n1.5log0.5n)-time algorithm that computes a non-crossing matching M of P, such that bn(M)≤210×bn(^MNC), where bn(M) is the length of a longest edge in M. An interesting implication of our construction is that bn(^MNC)/bn(^MC)≤210. Finally, we show that when the points of P are in convex position, one can compute ^MNC in O(ⁿ³) time, improving a result in [7].

Original language	English
Pages (from-to)	447-457
Number of pages	11
Journal	Computational Geometry: Theory and Applications
Volume	47
Issue number	3 PART A
DOIs	https://doi.org/10.1016/j.comgeo.2013.10.005
State	Published - 1 Jan 2014

Keywords

Approximation algorithms
Bottleneck matching
NP-hardness
Non-crossing configuration

ASJC Scopus subject areas

Computer Science Applications
Geometry and Topology
Control and Optimization
Computational Theory and Mathematics
Computational Mathematics

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10.1016/j.comgeo.2013.10.005

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title = "Bottleneck non-crossing matching in the plane",

abstract = "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 first prove that the problem is NP-hard and does not admit a PTAS. Then, we present an O(n1.5log0.5n)-time algorithm that computes a non-crossing matching M of P, such that bn(M)≤210×bn(MNC), where bn(M) is the length of a longest edge in M. An interesting implication of our construction is that bn(MNC)/bn(MC)≤210. Finally, we show that when the points of P are in convex position, one can compute MNC in O(n3) time, improving a result in [7].",

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T1 - Bottleneck non-crossing matching in the plane

AU - Karim Abu-Affash, A.

AU - Carmi, Paz

AU - Katz, Matthew J.

AU - Trabelsi, Yohai

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Y1 - 2014/1/1

N2 - 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 first prove that the problem is NP-hard and does not admit a PTAS. Then, we present an O(n1.5log0.5n)-time algorithm that computes a non-crossing matching M of P, such that bn(M)≤210×bn(MNC), where bn(M) is the length of a longest edge in M. An interesting implication of our construction is that bn(MNC)/bn(MC)≤210. Finally, we show that when the points of P are in convex position, one can compute MNC in O(n3) time, improving a result in [7].

AB - 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 first prove that the problem is NP-hard and does not admit a PTAS. Then, we present an O(n1.5log0.5n)-time algorithm that computes a non-crossing matching M of P, such that bn(M)≤210×bn(MNC), where bn(M) is the length of a longest edge in M. An interesting implication of our construction is that bn(MNC)/bn(MC)≤210. Finally, we show that when the points of P are in convex position, one can compute MNC in O(n3) time, improving a result in [7].

KW - Approximation algorithms

KW - Bottleneck matching

KW - NP-hardness

KW - Non-crossing configuration

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JO - Computational Geometry: Theory and Applications

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Bottleneck non-crossing matching in the plane

Abstract

Keywords

ASJC Scopus subject areas

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