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Analysis of probabilistic roadmaps for path planning
Provides an analysis of a path planning method which uses probabilistic roadmaps. This method has proven very successful in practice, but the theoretical understanding of its performance is stillExpand
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Analysis of probabilistic roadmaps for path planning
We provide an analysis of a recent path planning method which uses probabilistic roadmaps. This method has proven very successful in practice, but the theoretical understanding of its performance isExpand
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Multiple lattice tiles and Riesz bases of exponentials
Suppose $\Omega\subseteq\RR^d$ is a bounded and measurable set and $\Lambda \subseteq \RR^d$ is a lattice. Suppose also that $\Omega$ tiles multiply, at level $k$, when translated at the locationsExpand
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Fast Computation of the Euclidian Distance Maps for Binary Images
Abstract A simple algorithm is given for the computation of the Euclidian distance from the set of black points in an N × N black and white image, for all points in the image. The running time isExpand
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On the Structure of Multiple Translational Tilings by Polygonal Regions
Abstract. We consider polygons with the following ``pairing property'': for each edge of the polygon there is precisely one other edge parallel to it. We study the problem of when such a polygon KExpand
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Tiles with no spectra
Abstract We exhibit a subset of a finite Abelian group, which tiles the group by translation, and such that its tiling complements do not have a common spectrum (orthogonal basis for their L 2 spaceExpand
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Fuglede's conjecture on cyclic groups of order $p^nq$
Fuglede's conjecture on cyclic groups of order $p^nq$, Discrete Analysis 2017:12, 16 pp. A conjecture of Fuglede from 1974 states that a measurable set $E\subset \mathbb R^n$ of positive LebesgueExpand
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Structure of tilings of the line by a function
A function f 2 L 1 (R) tiles the line with a constant weight w using the discrete tile set A if P a2A f(x ? a) = w almost everywhere. A set A is of bounded density if there is a constant C such thatExpand
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The Density ofBh[g] Sequences and the Minimum of Dense Cosine Sums
A setEof integers is called aBh[g] set if every integer can be written in at mostgdifferent ways as a sum ofhelements ofE. We give an upper bound for the size of aBh[1] subset {n1, …,nk} of {1, …,n}Expand
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On the Steinhaus tiling problem
Several results are proved related to a question of Steinhaus: is there a set E ⊂ℝ 2 such that the image of E under each rigid motion of IR2 contains exactly one lattice point? AssumingExpand
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