Searching Two steps: filter (prune most of database) and refine ( find true answers) Range searching   Filter     Compute lower bounds for data points using cells     If lower bound , prune   Refine     Find actual distances for candidates not pruned in filter step Nearest neighbor searching   Filter     Compute lower and upper bounds for data points using cells     If lower bound upper bound of some other, prune   Refine     Find actual distances in increasing order of lower bound for candidates not pruned in filter step     If lower bound actual distance of some other, prune