ESA'11 Proceedings of the 19th European conference on Algorithms
Budget feasible mechanism design: from prior-free to bayesian
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
Single approximation for biobjective max TSP
WAOA'11 Proceedings of the 9th international conference on Approximation and Online Algorithms
Single approximation for the biobjective Max TSP
Theoretical Computer Science
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Many polynomial-time solvable combinatorial optimization problems become NP-hard if an additional complicating constraint is added to restrict the set of feasible solutions. In this paper, we consider two such problems, namely maximum-weight matching and maximum-weight matroid intersection with one additional budget constraint. We present the first polynomial-time approximation schemes for these problems. Similarly to other approaches for related problems, our schemes compute two solutions to the Lagrangian relaxation of the problem and patch them together to obtain a near-optimal solution. However, due to the richer combinatorial structure of the problems considered here, standard patching techniques do not apply. To circumvent this problem, we crucially exploit the adjacency relations on the solution polytope and, surprisingly, the solution to an old combinatorial puzzle.