This paper describes a technique for calculating the switching activity of a set of registers shared by dierent data values. Based on the assumption that the joint pdf (probability density function) of the primary input random variables is known or that a suciently 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 dened 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.