منابع مشابه
Cutting a Set of Disks by a Line with Leaving Many Intact Disks in Both Sides
Cut by a line the union of given disjoint disks in the plane so that both sides of the line contain many intact disks. At least how many intact disks can we leave in either side? It is proved that there is a family of infinitely many disjoint disks in the plane for which every line has a side that contains at most one intact disk. On the other hand, for any family of n disjoint disks, there is ...
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Artificial atoms are a cornerstone of emerging technologies that promise to make practical use of the laws of quantum mechanics. In principle, artificial atoms should behave like real atoms but be compatible with a solidstate environment. As such, they could serve as solidstate quantum bits (qubits) ideally suited to interfacing with photonic qubits. They could store, manipulate, and retrieve q...
متن کاملGeometric Unique Set Cover on Unit Disks and Unit Squares
We study the Unique Set Cover problem on unit disks and unit squares. For a given set P of n points and a set D of m geometric objects both in the plane, the objective of the Unique Set Cover problem is to select a subset D′ ⊆ D of objects such that every point in P is covered by at least one object in D′ and the number of points covered uniquely is maximized, where a point is covered uniquely ...
متن کاملPoint 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 an open problem raised in [1]. Using a similar reduction, we show that finding a minimum cardinali...
متن کاملDisjoint empty disks supported by a point set
For a planar point-set P , let D(P ) be the minimum number of pairwise-disjoint empty disks such that each point in P lies on the boundary of some disk. Further define D(n) as the maximum of D(P ) over all n-element point sets. Hosono and Urabe recently conjectured that D(n) = ⌈n/2⌉. Here we show that D(n) ≥ n/2 + n/236 − O(√n) and thereby disprove this conjecture.
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ژورنال
عنوان ژورنال: Nature Photonics
سال: 2006
ISSN: 1749-4885,1749-4893
DOI: 10.1038/nphoton.2006.67