The shuffling buffer

Olivier Devillers 1 Philippe Guigue 1
1 PRISME - Geometry, Algorithms and Robotics
CRISAM - Inria Sophia Antipolis - Méditerranée
Abstract : The complexity of randomized incremental algorithms is analyzed with the assumption of a random order of the input. To guarantee this hypothesis, the n data have to be known in advance in order to be mixed what contradicts with the on-line nature of the algorithm. We present the shuffling buffer technique to introduce sufficient randomness to guarantee an improvement on the worst case complexity by knowing only k data in advance. Typically, an algorithm with $O(n^2)$ worst-case complexity and O(n) or O(n log n) randomized complexity has an O((n^2 log k)/k) complexity for the shuffling buffer. We illustrate this with binary search trees, the number of Delaunay triangles or the number of trapezoids in a trapezoidal map created during an incremental construction.
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Olivier Devillers, Philippe Guigue. The shuffling buffer. International Journal of Computational Geometry and Applications, World Scientific Publishing, 2001, 11, pp.555-572. ⟨10.1142/S021819590100064X⟩. ⟨inria-00412567⟩

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