9. A computer-implemented method for processing a data stream associated with a given data stream application, comprising steps of: obtaining at least one range query associated with the data stream; and building a range query index based on the at least one range query using one or more virtual constructs such that the range query index is adaptive to one or more changes in a distribution of range query sizes; wherein building the range query index comprises decomposing the at least one range query into a minimal number of containment-encoded squares of varying sizes; wherein the range query index is configured to process at least a portion of the data stream associated with the given data stream application; and wherein the steps are performed by a computer system.
9. A computer-implemented method for processing a data stream associated with a given data stream application, comprising steps of: obtaining at least one range query associated with the data stream; and building a range query index based on the at least one range query using one or more virtual constructs such that the range query index is adaptive to one or more changes in a distribution of range query sizes; wherein building the range query index comprises decomposing the at least one range query into a minimal number of containment-encoded squares of varying sizes; wherein the range query index is configured to process at least a portion of the data stream associated with the given data stream application; and wherein the steps are performed by a computer system. 10. The method of claim 9 , wherein the step of building the range query index further comprises steps of: dividing a monitoring region associated with the at least one range query into one or more initial-level virtual squares; defining one or more levels of virtual squares for each of the initial-level virtual squares; decomposing the at least one range query into one or more of the virtual squares; and associating an identifier of the at least one range query with the one or more decomposed virtual squares.