The problem of allocating modules to processors in a distributed system to minimize total costs when the underlying communication graph is a partial k-tree and all costs are linear functions of a real parameter t is considered. It is shown that if the number of processors is fixed, the sequence of optimum assignments that are obtained as t varies from zero to infinity can be constructed in polynomial time. As an auxiliary result, a linear time separator algorithm for k-trees is developed. The implications of the results for parametric versions of the weighted vertex cover, independent set, and 0-1 quadratic programming problems on partial k-trees are discussed. >