Budgeted Matching via the Gasoline Puzzle

Guido Schäfer ()
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Guido Schäfer: Centrum Wiskunde & Informatica

A chapter in Gems of Combinatorial Optimization and Graph Algorithms, 2015, pp 49-57 from Springer

Abstract: 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.

Keywords: Feasible Solution; Match Problem; Lagrangian Relaxation; Minimum Span Tree Problem; Lagrangian Dual Problem (search for similar items in EconPapers)
Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-24971-1_5

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DOI: 10.1007/978-3-319-24971-1_5

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