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Many programs can be invoked under different execution options, input parameters and data files. Such different execution contexts may lead to strikingly different execution instances. The optimal code generation may be sensitive to the execution instances. In this paper, we show how to use parametric program analysis to deal with this issue for the optimization problem of computation offloading.Computation offloading has been shown to be an effective way to improve performance and energy saving on mobile devices. Optimal program partitioning for computation offloading depends on the tradeoff between the computation workload and the communication cost. The computation workload and communication requirement may change with different execution instances. Optimal decisions on program partitioning must be made at run time when sufficient information about workload and communication requirement becomes available.Our cost analysis obtains program computation workload and communication cost expressed as functions of run-time parameters, and our parametric partitioning algorithm finds the optimal program partitioning corresponding to different ranges of run-time parameters. At run time, the transformed program self-schedules its tasks on either the mobile device or the server, based on the optimal program partitioning that corresponds to the current values of run-time parameters. Experimental results on an HP IPAQ handheld device show that different run-time parameters can lead to quite different program partitioning decisions.