Abstract
We present an efficient method for maintaining a compressed quadtree for a set of moving points in ℝd. Our method works in the black-box KDS model, where we receive the locations of the points at regular time steps and we know a bound d max on the maximum displacement of any point within one time step. When the number of points within any ball of radius d max is at most k at any time, then our update algorithm runs in O(nlogk) time. We generalize this result to constant-complexity moving objects in ℝd. The compressed quadtree we maintain has size O(n); under similar conditions as for the case of moving points it can be maintained in O(n logλ) time per time step, where λ is the density of the set of objects. The compressed quadtree can be used to perform broad-phase collision detection for moving objects; it will report in O((λ + k)n) time a superset of all intersecting pairs of objects.
M. Roeloffzen and B. Speckmann were supported by the Netherlands’ Organisation for Scientific Research (NWO) under project no. 600.065.120 and 639.022.707, respectively.
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de Berg, M., Roeloffzen, M., Speckmann, B. (2012). Kinetic Compressed Quadtrees in the Black-Box Model with Applications to Collision Detection for Low-Density Scenes. In: Epstein, L., Ferragina, P. (eds) Algorithms – ESA 2012. ESA 2012. Lecture Notes in Computer Science, vol 7501. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33090-2_34
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DOI: https://doi.org/10.1007/978-3-642-33090-2_34
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