1. A computer-implemented method comprising: receiving, by one or more computing systems configured to provide a program execution service that executes programs for multiple users by using a plurality of computing nodes provided by the program execution service, configuration information regarding using indicated input data as part of executing an indicated program for a first user of the multiple users in a distributed manner on a computing node cluster; selecting, by the one or more configured computing systems, multiple computing nodes from the plurality for the computing node cluster based at least in part on the selected multiple computing nodes each being identified as locally storing at least some of the indicated input data prior to the receiving of the configuration information; determining, by the one or more configured computing systems and based on at least one of the selected multiple computing nodes being currently unavailable to perform the executing of the indicated program due to executing one or more other programs for one or more other users and based on the executing of the indicated program being determined to have a higher priority than the executing of the one or more other programs, to terminate the executing of the one or more other programs on the at least one selected computing node to enable use of the at least one selected computing node in the executing of the indicated program; and initiating, by the one or more configured computing systems and based at least in part on the terminating of the executing of the one or more other programs on the at least one selected computing node, the executing of the indicated program on the selected multiple computing nodes using the locally stored at least some indicated input data.