Abstract: Disclosed are techniques for implementing physics aware model reduction for a design. These techniques identify a design model and generate a first set of solutions with a first discretization scheme and a plurality of inputs. A second discretization scheme may be generated at least by performing geometry simplification and re-discretization based in part or in whole on one or more distributions from the first set of solution. With the second discretization scheme, a second set of solutions may be generated with the second discretization scheme and the plurality of inputs.

Abstract: Systems and methods for performing a mobile range query are provided. A system can include a first computer readable medium configured to iteratively transmit a mobile range query, as well as a second computer readable medium configured to: receive a mobile range query; compute a range query result; build two min-heaps that contain in-border interest points and out-border intersect points respectively; construct an initial candidate safe region by popping top elements in the two min-heaps while they are not empty; computing the intersections of the domain region of the top elements and the candidate safe region and redefining the candidate safe region using the intersections; and return the mobile range query results to the first medium.

Abstract: Systems and methods for performing a mobile window query are provided. A method can include transmitting a mobile window query, determining which interest point falls within a query window, defining a potential safe region, refining the safe region utilizing the surrounding interest points, and returning the interest points and safe region to a user.

Abstract: Methods and apparatuses for providing a k-nearest neighbor for location based services are provided. A method can include querying a database to detect a plurality of interest points within a predetermined distance of the user device using a kNN algorithm, organizing the interest points within a Voronoi tree, and continuously return a position specific result of relevant interest points.

Abstract: Methods for progressive continuous range query (PCRQ) are provided. A method can include using branch-and-bound to index interest points with a tree-index and generating a nearest enter split-point for a root node in the tree-index and adding to min-heap. Next, whether min-heap has more elements and whether a next split-point in min-heap is closer than a destination can be determined. Whether a query point has reached a split-point can be investigated followed by retrieving an entry that has generated the split-point. The split-point can be then be removed from min-heap.