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On isolating points using unit disks
Journal article   Open access

On isolating points using unit disks

Matt Gibson, Gaurav Kanade, Rainer Penninger, Kasturi Varadarajan and Ivo Vigan
Journal of computational geometry, Vol.7(1), pp.540-557
12/01/2016
DOI: 10.20382/jocg.v7i1a22
url
https://doi.org/10.20382/jocg.v7i1a22View
Published (Version of record) Open Access

Abstract

Given a set of points in the plane and a set of disks which separate the points, we consider the problem of selecting a minimum size subset of the disks such that any path between any pair of points is intersected by at least one of the selected disks. We present a (9 + epsilon)-approximation algorithm for this problem and show that it is NP-complete even if all disks have unit radius and no disk contains any points. Using a similar reduction, we further show that the Multiterminal Cut problem [9] remains NP-complete on unit disk graphs. Lastly, we prove that removing a minimum subset of a collection of unit disks, such that the plane minus the arrangement of the remaining disks consists of a single connected region is also NP-complete.
Mathematics Physical Sciences Science & Technology

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