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 d . 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 R d . 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¿) time per time step, where ¿ 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((¿¿+¿k)n) time a superset of all intersecting pairs of objects