Dec 21, 2009 · We prove the existence of a distance k-sector for all k and for every two disjoint, nonempty, closed sets P and Q in Euclidean spaces of any ( ...

Distance k-sectors exist. The bisector of two nonempty sets P and Q in R^d is the set of all points with equal distance to P and to Q. · Zone diagrams in ...

We prove the existence of a distance k-sector for all k and for every two disjoint, nonempty, closed sets P and Q in Euclidean spaces of any (finite) dimension.

The existence of a distance k-sector for all k and for every two disjoint, nonempty, closed sets P and Q in Euclidean spaces of any (finite) dimension is ...

We prove the existence of a distance k-sector for all k and for every two disjoint, nonempty, closed sets P and Q in Euclidean spaces of any (finite) dimension ...

We prove the existence of a distance k-sector for all k and for every two disjoint, nonempty, closed sets P and Q in Euclidean spaces of any (finite) dimension ...

Distance k-sectors were introduced by Asano et al. ... We give the first proof of existence of k-sectors in Eu- clidean spaces for a general k. ... Note that a k- ...

We also show the existence of a distance k-sector between two sites. Both proofs rely on the Knaster–Tarski theorem on fixed points of monotone functions. 1 ...

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Abstract. The (distance) k-sector is a generalization of the concept of bisectors proposed by Asano, Matoušek and Tokuyama. We prove the.