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Budgeted Matching via the Gasoline Puzzle

In: Gems of Combinatorial Optimization and Graph Algorithms

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  • Guido Schäfer

    (Centrum Wiskunde & Informatica
    VU University Amsterdam)

Abstract

We consider a natural generalization of the classical matching problem: In the budgeted matching problem we are given an undirected graph with edge weights, non-negative edge costs and a budget. The goal is to compute a matching of maximum weight such that its cost does not exceed the budget. This problem is weakly NP-hard. We present the first polynomial-time approximation scheme for this problem. Our scheme computes two solutions to the Lagrangian relaxation of the problem and patches them together to obtain a near-optimal solution. In our patching procedure we crucially exploit the adjacency relations of vertices of the matching polytope and the solution to an old combinatorial puzzle.

Suggested Citation

  • Guido Schäfer, 2015. "Budgeted Matching via the Gasoline Puzzle," Springer Books, in: Andreas S. Schulz & Martin Skutella & Sebastian Stiller & Dorothea Wagner (ed.), Gems of Combinatorial Optimization and Graph Algorithms, pages 49-57, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-24971-1_5
    DOI: 10.1007/978-3-319-24971-1_5
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