Kinetic Compressed Quadtrees in the Black-Box Model with Applications to Collision Detection for Low-Density Scenes

We present an efficient method for maintaining a compressed quadtree for a set of moving points in R. Our method works in the blackbox KDS model, where we receive the locations of the points at regular time steps and we know a bound dmax on the maximum displacement of any point within one time step. When the number of points within any ball of radius dmax is at most k at any time, then our update algorithm runs in O(n log k) time. We generalize this result to constant-complexity moving objects in R. 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 log λ) time per time step, where λ is the density of the set of objects. The compressed quadtree can be used to perform broadphase collision detection for moving objects; it will report in O((λ+k)n) time a superset of all intersecting pairs of objects.