On the Planar Two-Center Problem and Circular Hulls

Wang, Haitao

doi:10.1007/s00454-021-00358-5

Cited by 8 publications

(13 citation statements)

References 30 publications

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“…Our algorithm works as follows. It follows the framework by Wang [15] (and thus by Chan [2]). It uses the O(n)-time sequential decision algorithm by Wang.…”

Section: Our Resultsmentioning

confidence: 96%

“…But Tan [14] pointed out a mistake in the time analysis, and presented an O(n log 2 n)-time algorithm for the problem. But Wang [15] showed a counterexample to the algorithm by Tan, and gave an O(n log n log log n)-time algorithm for this problem [15].…”

Section: Our Resultsmentioning

confidence: 99%

“…Wang gave an O(n log n log log n)-time algorithm for the restricted 2-center problem [15], combining the circular hull and parametric search by Cole [3]. The parametric search paradigm consists of a sequential algorithm and a parallel algorithm.…”

Section: Preliminariesmentioning

confidence: 99%

“…Since then there is no improvement over 20 years until Wang [15] very recently gave an O(n log n log log n)-time deterministic algorithm for the restricted 2-center problem, improving on Chan's method by a log n log log n factor. Combining Eppstein's O(n log 2 n)-time algorithm for the well-separated case, the planar 2-center problem can be solved in O(n log 2 n) time deterministically.…”

Section: Introductionmentioning

confidence: 99%

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Efficient Planar Two-Center Algorithms

Choi¹,

Ahn²

2020

Preprint

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We consider the planar Euclidean two-center problem in which given n points in the plane find two congruent disks of the smallest radius covering the points. We present a deterministic O(n log n)-time algorithm for the case that the centers of the two optimal disks are close together, that is, the overlap of the two optimal disks is a constant fraction of the disk area. This improves the previous best O(n log n log log n) bound by Wang for the case. We also present a deterministic O(n log n)-time algorithm for the case that the input points are in convex position.

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“…Our algorithm works as follows. It follows the framework by Wang [15] (and thus by Chan [2]). It uses the O(n)-time sequential decision algorithm by Wang.…”

Section: Our Resultsmentioning

confidence: 96%

Section: Our Resultsmentioning

confidence: 99%

Section: Preliminariesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Efficient Planar Two-Center Algorithms

Choi¹,

Ahn²

2020

Preprint

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show abstract

“…The covering problem has been extensively studied in the context of the k-center problem and the facility location problem when the region to cover is a set of points and the predefined shape is a disk in the plane. In last decades, there have been a lot of works, including exact algorithms for k = 2 [3,12,14,15,34,36], exact and approximation algorithms for large k [2,20,22,25],…”

Section: Introductionmentioning

confidence: 99%