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Preprint 49-2007

Combinatorial Optimization & Graph Algorithms group (COGA-Preprints)

Budgeted Matching and Budgeted Matroid Intersection via the Gasoline Puzzle
Andre Berger, Vincenzo Bonifaci, Fabrizio Grandoni, and Guido Schäfer
not available
combinatorial optimization, approximation algorithms, matching, matroid intersection, polynomial-time approximation scheme
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 poly-nomial-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. 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, somewhat surprisingly, the solution to an old combinatorial puzzle.
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