An efficient algorithm for the Euclidean two-center problem

Jaromczyk, Jerzy W.; Kowaluk, Mirosław

doi:10.1145/177424.178038

Cited by 37 publications

(20 citation statements)

References 9 publications

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“…The runtime of the decision algorithm of Agarwal and Sharir was improved by Hershberger [5] to 2 ( ) O n . Jaromczyk and Kowaluk [6] use the algorithm by Hershberger [5] to obtain an 2 ( log ) O n n running time algorithm for the two-center problem. A major progress on this problem was recently made by Sharir [7], who presented an 9 ( log ) O n n -time algorithm, by combining the parametric search technique with several additional techniques, including a variant of the matrix search algorithm of Frederickson and Johnson [8].…”

Section: Two-sensor Problemmentioning

confidence: 99%

2-Sensor Problem

Segal¹

2004

Sensors

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Ad-hoc networks of sensor nodes are in general semi-permanently deployed. However, the topology of such networks continuously changes over time, due to the power of some sensors wearing out to new sensors being inserted into the network, or even due to designers moving sensors around during a network re-design phase (for example, in response to a change in the requirements of the network). In this paper, we address the problem of covering a given path by a limited number of sensors -in our case to two, and show its relation to the well-studied matrix multiplication problem.

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Section: Two-sensor Problemmentioning

confidence: 99%

2-Sensor Problem

Segal¹

2004

Sensors

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“…Using this result and with parametric search technique [16], Agarwal and Sharir [1] gave an O(n 2 log 3 n) time algorithm for the planar 2-center problem. Later, Jaromczyk and Kowaluk [15] proposed an O(n 2 ) time algorithm. A breakthrough was achieved by Sharir [18], who gave the first-known subquadratic algorithm for the problem, and the running time is O(n log 9 n).…”

Section: Introductionmentioning

confidence: 99%

Improved Algorithms for the Bichromatic Two-Center Problem for Pairs of Points

Wang

Xue

2019

Lecture Notes in Computer Science

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We consider a bichromatic two-center problem for pairs of points. Given a set S of n pairs of points in the plane, for every pair, we want to assign a red color to one point and a blue color to the other, in such a way that the value max{r1, r2} is minimized, where r1 (resp., r2) is the radius of the smallest enclosing disk of all red (resp., blue) points. Previously, an exact algorithm of O(n 3 log 2 n) time and a (1 + ε)approximate algorithm of O(n + (1/ε) 6 log 2 (1/ε)) time were known. In this paper, we propose a new exact algorithm of O(n 2 log 2 n) time and a new (1 + ε)-approximate algorithm of O(n + (1/ε) 3 log 2

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“…This problem has been well studied in both the exact (2,7,8,9,10,11,13,21,25] and approximate [10,12,18] versions. In approximate versions a set P provides (1 +c)-approximate k-center if the associated radius is at most (1 +c) times the optimal radius, for any c > 0.…”

Section: Introductionmentioning

confidence: 99%

Lower and Upper Bounds for Tracking Mobile Users

Bespamyatnikh

Bhattacharya

Kirkpatrick

et al. 2002

Foundations of Information Technology in the Era of Network and Mobile Computing

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In this paper we prove improved lower and upper bounds for the location of mobile facilities (in Loo and L2 metrics) under the motion of clients when facility moves faster than clients. This paper continues the research started in our joint paper where we present lower bounds and efficient algorithms for exact and approximate maintenance of the 1-center for a set of moving points in the plane. Our algorithms are based on the kinetic framework introduced by Basch, Guibas and Hershberger.R.

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An efficient algorithm for the Euclidean two-center problem

Cited by 37 publications

References 9 publications

2-Sensor Problem

2-Sensor Problem

Improved Algorithms for the Bichromatic Two-Center Problem for Pairs of Points

Lower and Upper Bounds for Tracking Mobile Users

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