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- W2562901933 abstract "Given a set of points in the plane and a set of disks (that we think of as wireless sensors) which separate the points, we consider the problem of selecting a minimum 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 hardness reduction, we further show that the Multiterminal Cut problem 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." @default.
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- W2562901933 date "2016-12-29" @default.
- W2562901933 modified "2023-09-24" @default.
- W2562901933 title "On isolating points using unit disks" @default.
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- W2562901933 doi "https://doi.org/10.20382/jocg.v7i1a22" @default.
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