Randomized multidimensional search trees: further results in dynamic sampling

The use of randomization in dynamic search structures by means of a technique called dynamic sampling is investigated. In particular, an efficient algorithm for dynamic (logarithmic time) point location in 3-D partitions induced by a set of possibly interesting polygons in R ³ is given. The expected running time of the algorithm on a random sequence of updates is close to optimal. Efficient algorithms for dynamic nearest-k-neighbor queries and half space range queries in R^d are also given