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In this paper, we present an approach for the calculation of lower and upper bounds on the power consumption of data path resources like functional units, registers, I/O ports, and busses from scheduled data flow graphs executing a specified input data stream. The low power allocation and binding problem is formulated. First, it is shown that this problem without constraining the number of resources can be relaxed to the bipartite weighted matching problem which is solvable in O(n)/sup 3/. n is the number of arithmetic operations, variables, I/O-access or bus-access operations which have to be bound to data path resources. In a second step we demonstrate that the relaxation can be efficiently extended by including Lagrange multipliers in the problem formulation to handle a resource constraint. The estimated bounds take into account the effects of resource sharing. The technique can be used, for example, to prune the design space in high-level synthesis for low power before the allocation and binding of the resources. The application of the technique on benchmarks with real application input data shows the tightness of the bounds.