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Finding tradeoffs in design space is naturally formulated as a multicriteria optimization problem. In this paper, we model tradeoffs between communication cost and the balance of processor workloads for the problem of mapping applications to processors in a multicore environment. We formulate several query strategies for finding Pareto optimal and approximately Pareto optimal solutions to the mapping problem using a constraint solver as a time-bounded oracle. Each of the strategies directs the oracle through the search space in a different manner. We evaluate the efficiency of these strategies on a series of synthetic benchmarks, and on two industrial applications, a video noise reduction, and an image demosaic color filtering. The results indicate a significant tradeoff between precision and computation time, and a corresponding benefit to time-bounded queries.