The maximin line problem with regional demand

Díaz-Báñez, José Miguel; Ramos, Pedro; Sabariego, Pilar

doi:10.1016/j.ejor.2006.06.013

Cited by 6 publications

(1 citation statement)

References 36 publications

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“…The max-min line location problem is also known as the obnoxious line location problem, shortly the OLL problem, and was first studied by Drezner and Wesolowsky 7 with an O(n 3 )time algorithm. The first near-quadratic O(n 2 log 3 n)-time algorithm was recently presented by Díaz-Báñez et al; 8 later, Chen and Wang 9 improved it to O(n 2 log n) time. Both algorithms are based on parametric search technique.…”

Section: Introductionmentioning

confidence: 99%

The Onion Diagram: A Voronoi-Like Tessellation of a Planar Line Space and Its Applications

Bae

Shin

2012

Int. J. Comput. Geom. Appl.

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Given a set S of weighted points in the plane, we consider two problems dealing with lines in R 2 under the weighted Euclidean distance: (1) Preprocess S into a data structure that efficiently finds a nearest point among S to a query line. (2) Find an optimal line that maximizes the minimum of the weighted distance to any point of S. The latter problem is also known as the obnoxious line location problem. We introduce a unified approach to both problems based on a new geometric transformation that maps lines in the plane to points in a line space. It turns out that our transformation, together with its target space, well describes the proximity relations between given weighted points S and every line in R 2 . We define a Voronoi-like tessellation on the line space and investigate its geometric, combinatorial, and computational properties. As its direct applications, we obtain several new algorithmic results on the two problems. We also show that our approach extends to weighted line segments and weighted polygons.

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Section: Introductionmentioning

confidence: 99%