Maximum Centre-Disjoint Mergeable Disks

Given a set of disks in the plane, the goal of the problem studied in this paper is to choose a subset of these disks such that none of its members contains the centre of any other. Each disk not in this subset must be merged with one of its nearby disks that is, increasing the latter's radius....

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Bibliographic Details
Published in:arXiv.org 2024-12
Main Author: Ali Gholami Rudi
Format: Article
Language:English
Subjects:
Algorithms
Disks
Polynomials
Online Access:Get full text
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Summary:Given a set of disks in the plane, the goal of the problem studied in this paper is to choose a subset of these disks such that none of its members contains the centre of any other. Each disk not in this subset must be merged with one of its nearby disks that is, increasing the latter's radius. This problem has applications in labelling rotating maps and in visualizing the distribution of entities in static maps. We prove that this problem is NP-hard. We also present an ILP formulation for this problem, and a polynomial-time algorithm for the special case in which the centres of all disks are on a line.
ISSN:2331-8422