1. A method for operating a data processing system, comprising: retrieving a thread for execution by at least one processor core of a plurality of processor cores connected to a data memory structure, wherein the data memory structure includes: one or more dedicated Level-1 data caches included in each of the plurality of processor cores, and a combined memory hierarchy physically connected to the one or more dedicated Level-1 data caches, the combined memory hierarchy having one or more shared higher level caches and a main memory, wherein the one or more shared higher level caches are at a level above the one or more dedicated Level-1 data caches; executing the thread, including associating tag information with data transmitted within the data memory structure, wherein the tag information is stored in respective Level-1 data caches of the one or more dedicated Level-1 data caches, and wherein the tag information defines a movement of the associated data in the data memory structure between the one or more shared higher level caches of the combined memory hierarchy; and managing, based on the tag information, at least one of: transmission of the data within the combined memory hierarchy, and transmission of the data between the combined memory hierarchy and one or more of the plurality of processor cores.