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<p>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.</p>
module allocation; partial k-trees; communication graph; polynomial time; computational complexity; distributed processing; dynamic programming; graph theory; resource allocation.

A. Medepalli and D. Fernandez-Baca, "Parametric Module Allocation on Partial k-Trees," in IEEE Transactions on Computers, vol. 42, no. , pp. 738-742, 1993.
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