On generating all maximal independent sets
Information Processing Letters
Journal of Symbolic Computation
A polynomial time algorithm for counting integral points in polyhedra when the dimension is fixed
Mathematics of Operations Research
Integer Polynomial Optimization in Fixed Dimension
Mathematics of Operations Research
Computing pure strategy nash equilibria in compact symmetric games
Proceedings of the 11th ACM conference on Electronic commerce
Rational Generating Functions and Integer Programming Games
Operations Research
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We settle the computational complexity of fundamental questions related to multicriteria integer linear programs, when the dimensions of the strategy space and of the outcome space are considered fixed constants. In particular we construct: (1) polynomial-time algorithms to determine exactly the number of Pareto optima and Pareto strategies; (2) a polynomial-space polynomial-delay prescribed-order enumeration algorithm for arbitrary projections of the Pareto set; (3) a polynomial-time algorithm to minimize the distance of a Pareto optimum from a prescribed comparison point with respect to arbitrary polyhedral norms; and (4) a fully polynomial-time approximation scheme for the problem of minimizing the distance of a Pareto optimum from a prescribed comparison point with respect to the Euclidean norm.