Efficient Algorithm for Placing Base Stations by Avoiding Forbidden Zone

Roy, Sasanka; Bardhan, Debabrata; Das, Sandip

doi:10.1007/11604655_14

Cited by 3 publications

(3 citation statements)

References 11 publications

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“…Other variations have also been considered [11][12][13] for k = 1. For k ≥ 2, variants have been studied, as this has applications to the placement of base stations in wireless sensor networks [14][15][16][17] and privacy preserving in social networks [18]. Another variant is the α-connected twocenter problem, where the goal is to find two balls of minimum radius r whose union covers the points, and the distance of the two centers is at most 2(1 − α)r, for 0 ≤ α ≤ 1.…”

Section: Introductionmentioning

confidence: 99%

Red–Blue k-Center Clustering with Distance Constraints

et al. 2023

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We consider a variant of the k-center clustering problem in IRd, where the centers can be divided into two subsets—one, the red centers of size p, and the other, the blue centers of size q, such that p+q=k, and each red center and each blue center must be a distance of at least some given α≥0 apart. The aim is to minimize the covering radius. We provide a bi-criteria approximation algorithm for the problem and a polynomial time algorithm for the constrained problem where all centers must lie on a given line ℓ. Additionally, we present a polynomial time algorithm for the case where only the orientation of the line is fixed in the plane (d=2), although the algorithm works even in IRd by constraining the line to lie in a plane and with a fixed orientation.

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Section: Introductionmentioning

confidence: 99%

Red–Blue k-Center Clustering with Distance Constraints

et al. 2023

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“…For k ≥ 2, there are a few results [8,22,25] which have been done mostly for the base station placement problem in wireless sensor network. Das et al [22] studied more constrained problems where the k centers lie on a specific edge of a convex polygon and the corresponding disks cover all n vertices of the polygon. Their algorithm runs in O(min(n 2 , nk log n)) time.…”

Section: Introductionmentioning

confidence: 99%

“…Their algorithm runs in O(min(n 2 , nk log n)) time. In [22,25], they considered different constrained 2-center problems in which the centers lie in a convex polygon [25] or on a pair of specified edges of the convex polygon [22], but the two disks should cover all points in the polygon, i.e., the convex polygon itself.…”

Section: Introductionmentioning

confidence: 99%

Computing k-Centers On a Line

Brass,

Knauer,

et al. 2009

Preprint

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In this paper we consider several instances of the k-center on a line problem where the goal is, given a set of points S in the plane and a parameter k ≥ 1, to find k disks with centers on a line ℓ such that their union covers S and the maximum radius of the disks is minimized. This problem is a constraint version of the well-known k-center problem in which the centers are constrained to lie in a particular region such as a segment, a line, and a polygon.We first consider the simplest version of the problem where the line ℓ is given in advance; we can solve this problem in O(n log 2 n) time. We then investigate the cases where only the orientation of the line ℓ is fixed and where the line ℓ can be arbitrary. We can solve these problems in O(n 2 log 2 n) time and in O(n 4 log 2 n) expected time, respectively. For the last two problems, we present (1 + ε)-approximation algorithms, which run in O( 1ε n log 2 n) time and O( 1 ε 2 n log 2 n) time, respectively.

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Separated Red Blue Center Clustering

Eskandari,

Khare,

Kumar

2021

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Efficient Algorithm for Placing Base Stations by Avoiding Forbidden Zone

Cited by 3 publications

References 11 publications

Red–Blue k-Center Clustering with Distance Constraints

Red–Blue k-Center Clustering with Distance Constraints

Computing k-Centers On a Line

Separated Red Blue Center Clustering

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