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This paper describes a technique for calculating the switching activity of a set of registers shared by di erent data values. Based on the assumption that the joint pdf (probability density function) of the primary input random variables is known or that a su ciently large number of input vectors has been given, the register assignment problem for minimum power consumption is formulated as a minimum cost clique covering of an appropriately de ned compatibility graph (which is shown to be transitively orientable). The problem is then solved optimally (in polynomial time) using a max-cost ow algorithm. Experimental results conrm the viability and usefulness of the approach in minimizing power consumption during the register assignment phase of the behavioral synthesis process.