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Grid environments are becoming cost-effective substitutes to supercomputers. Datacutter is one of several initiatives in creating mechanisms for applications to efficiently exploit the vast computation power of such environments. In Datacutter, applications are modeled as a set of communicating filters that may run on several nodes of a computational grid. To achieve high performance, a number of transparent copies of each of the filters that comprise the application need to be appropriately placed on different nodes of the grid. Such task is carried out by a scheduler which is the focus of this work. We present LPSched, a scheduler for Datacutter applications which uses linear programming to make decisions about the number of copies of each filter as well as the placement of each of the copies across the nodes. LPSched bases its decisions upon the performance behavior of each filter as well as the resources currently available on the grid.