1. A computer-implemented method for managing execution of programs by a program execution service, the program execution service using a plurality of computing systems to execute programs, the plurality of computing systems including multiple groups of computing systems such that the computing systems of each group are physically proximate and share a common group data exchange medium that is specific to that group and such that the multiple groups of computing systems are connected via one or more other data exchange mediums distinct from the group data exchange mediums, the method comprising: receiving multiple requests that are each to execute an indicated one of multiple programs previously supplied to the program execution service, at least some of the multiple programs each having one or more copies stored locally on one or more of the plurality of computing systems; and for each received request to execute an indicated program, automatically satisfying the request by, automatically selecting at least one of the plurality of computing systems to use in executing an instance of the indicated program, the selecting of the at least one computing systems being based at least in part on whether the selected computing systems are in groups with one or more other systems that store local copies of the indicated program; and for each of the selected computing systems, if the selected computing system is in a group with one or more other systems that store a local copy of the indicated program, instructing the selected computing system to obtain a copy of the indicated program from at least one of the one or more other systems via the shared common group data exchange medium for the group and to initiate execution of the obtained program copy; and if the selected computing system is not in a group with another system that stores a local copy of the one program, instructing the selected computing system to obtain a copy of the indicated program from one or more remote systems via at least one of the one or more distinct data exchange mediums and to initiate execution of the obtained program copy, the automatic selecting and instructing being performed by one or more programmed computing systems.