Michal Kleinbort

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Sampling-based motion-planning algorithms typically rely on nearest-neighbor (NN) queries when constructing a roadmap. Recent results suggest that in various settings NN queries may be the computational bottleneck of such algorithms. Moreover, in several asymptotically-optimal algorithms these NN queries are of a specific form: Given a set of points and a(More)
We present a major revamp of the point-location data structure for general two-dimensional subdivisions via randomized incremental construction, implemented in Cgal, the Computational Geometry Algorithms Library. We can now guarantee that the constructed directed acyclic graph G is of linear size and provides logarithmic query time. Via the construction of(More)
The complexity of nearest-neighbor search dominates the asymptotic running time of many sampling-based motion-planning algorithms. However, collision detection is often considered to be the computational bottleneck in practice. Examining various asymptotically optimal planning algorithms, we characterize settings, which we call NNsensitive, in which the(More)
Given a planar map of n segments in which we wish to efficiently locate points, we present the first randomized incremental construction of the well-known trapezoidal-map search-structure that only requires expected O(n logn) preprocessing time while deterministically guaranteeing worst-case linear storage space and worst-case logarithmic query time. This(More)
This thesis studies theoretical and practical aspects of the computation of planar polygonal Minkowski sums via convolution methods. In particular we prove the “Convolution Theorem”, which is fundamental to convolution based methods, for the case of simple polygons. To the best of our knowledge this is the first complete proof for this case. Moreover, we(More)
We present a major revamp of the point-location data structure for general two-dimensional subdivisions via randomized incremental construction, implemented in Cgal, the Computational Geometry Algorithms Library. We can now guarantee that the constructed directed acyclic graph G is of linear size and provides logarithmic query time. Via the construction of(More)
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