Point Set Isolation Using Unit Disks is NP-complete
Computational Geometry
2013-03-13 v1
Abstract
We consider the situation where one is given a set S of points in the plane and a collection D of unit disks embedded in the plane. We show that finding a minimum cardinality subset of D such that any path between any two points in S is intersected by at least one disk is NP-complete. This settles an open problem raised by Matt Gibson et al[1]. Using a similar reduction, we show that finding a minimum cardinality subset D' of D such that R^2 - (D - D') consists of a single connected region is also NP-complete. Lastly, we show that the Multiterminal Cut Problem remains NP-complete when restricted to unit disk graphs.
Cite
@article{arxiv.1303.2779,
title = {Point Set Isolation Using Unit Disks is NP-complete},
author = {Rainer Penninger and Ivo Vigan},
journal= {arXiv preprint arXiv:1303.2779},
year = {2013}
}