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We present a method to design parallel algorithms for constrainedcombinatorial optimization problems. Our method solves and generalizes manyclassical combinatorial optimization problems including the stable marriageproblem, the shortest path problem and the market clearing price problem. Thesethree problems are solved in the literature using Gale-Shapley algorithm,Dijkstra's algorithm, and Demange, Gale, Sotomayor algorithm. Our method solvesall these problems by casting them as searching for an element that satisfiesan appropriate predicate in a distributive lattice. Moreover, it solvesgeneralizations of all these problems - namely finding the optimal solutionsatisfying additional constraints called {\em lattice-linear} predicates. Forstable marriage problems, an example of such a constraint is that Peter'sregret is less than that of Paul. For shortest path problems, an example ofsuch a constraint is that cost of reaching vertex $v_1$ is at least the cost ofreaching vertex $v_2$. For the market clearing price problem, an example ofsuch a constraint is that $item_1$ is priced at least as much as $item_2$. Inaddition to finding the optimal solution, our method is useful in enumeratingall constrained stable matchings, and all constrained market clearing pricevectors.

Applying Predicate Detection to the Constrained Optimization Problems