Point Set Isolation Using Unit Disks is NP-complete
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 a...
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| creator | Penninger, Rainer Vigan, Ivo |
| description | 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. |
| doi_str_mv | 10.48550/arxiv.1303.2779 |
| format | Article |
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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.</description><identifier>DOI: 10.48550/arxiv.1303.2779</identifier><language>eng</language><subject>Computer Science - Computational Geometry</subject><creationdate>2013-03</creationdate><rights>http://arxiv.org/licenses/nonexclusive-distrib/1.0</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,776,881</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/1303.2779$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.1303.2779$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Penninger, Rainer</creatorcontrib><creatorcontrib>Vigan, Ivo</creatorcontrib><title>Point Set Isolation Using Unit Disks is NP-complete</title><description>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
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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.</abstract><doi>10.48550/arxiv.1303.2779</doi><oa>free_for_read</oa></addata></record> |
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| subjects | Computer Science - Computational Geometry |
| title | Point Set Isolation Using Unit Disks is NP-complete |
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