Finding the minimum number of disks of fixed radius needed to cover a set of points in the plane by MaxiMinMax approach

Panov, Stefan; Panova, Svetlana; Garbev, Atanas

doi:10.1109/icai55857.2022.9960053

Cited by 2 publications

(3 citation statements)

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“…Let E min be the global minimum of the energy, i.e. (5) Now the problem under consideration can be formulated in the following way. Find a configuration of disks α such that E(α)=E min , (6) The configuration α minimizes the energy and therefore it maximizes the number of covered points.…”

Section: Experimental Mathematical Formulation Of the Problemmentioning

confidence: 99%

“…The considered problem is a variant of the unit disc cover problem (UDC) [1 -3] and the minimum geometric disk cover problem (MGDC) [4,5]. Such problems are known to be NP-complete [6].…”

Section: Introductionmentioning

confidence: 99%

“…Such problems are known to be NP-complete [6]. For this reason, in the literature, mainly algorithms that find only approximate solutions are available [3,5]. This work proposes a Monte Carlo algorithm that is capable of finding, with high degree of certainty, exact solutions of the problem.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Covering a Maximum Number of Points by a Fixed Number of Equal Disks via Simulated Annealing

Tomova,

Filipov,

Avdzhieva

2024

JCTM

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The presented paper considers the problem of covering a maximum number of n given points in the plane by m equal disks of radius r. A point is covered if it is inside one or more than one disk. The disks need to be placed in the plane in such a way that a maximum number of points are covered. To solve the problem, an objective function, called energy, is introduced in such a way that the greater the covering is, the lower the energy is. Thus, a configuration of disks with minimum energy is a configuration with maximum covering. To find a configuration of disks that minimizes the energy, a stochastic algorithm based on the Monte Carlo simulated annealing technique is proposed. The algorithm overcomes potential local minima, which, as shown in the paper, are quite likely to occur. The computational complexity of the algorithm is O(mn). The algorithm is tested on several cases demonstrating its efficiency in finding global minima of the energy, i.e. configurations with maximum covering.

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Section: Experimental Mathematical Formulation Of the Problemmentioning

confidence: 99%

“…The considered problem is a variant of the unit disc cover problem (UDC) [1 -3] and the minimum geometric disk cover problem (MGDC) [4,5]. Such problems are known to be NP-complete [6].…”

Section: Introductionmentioning

confidence: 99%