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 incremen-tal 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)
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 log n) preprocessing time while deterministically guaranteeing worst-case linear storage space and worst-case logarithmic query time. This(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 NN-sensitive, in which the(More)
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