We present a new approach for approximate nearest neighbor queries for sets of high dimensional points under any L/sub t/-metric, t=1,...,/spl infin/. The proposed algorithm is efficient and simple to implement. The algorithm uses multiple shifted copies of the data points and stores them in up to (d+1) B-trees where d is the dimensionality of the data, sorted according to their position along a space filling curve. This is done in a way that allows us to guarantee that a neighbor within an O(d/sup 1+1/t/) factor of the exact nearest, can be returned with at most (d+1)log, n page accesses, where p is the branching factor of the B-trees. In practice, for real data sets, our approximate technique finds the exact nearest neighbor between 87% and 99% of the time and a point no farther than the third nearest neighbor between 98% and 100% of the time. Our solution is dynamic, allowing insertion or deletion of points in O(d log/sub p/ n) page accesses and generalizes easily to find approximate k-nearest neighbors.

A productivity-driven methodology for incremental floorplanning is described and the constrained polygon transformation problem , a key step of this methodology, is formulated. The input to the problem consists of a floorplan computed using area estimates and the actual area required for each subcircuit of the floorplan. Informally, the objective is to change the areas of the modules without drastically changing their shapes or locations. We show that the constrained polygon transformation problem is NP-hard and present several fast algorithms that produce results within a few percent of a theoretical lower bound on several floorplans.