NDLI: Budgeted matching and budgeted matroid intersection via the gasoline puzzle

Content Provider	Springer Nature Link
Author	Bonifaci, Vincenzo Schäfer, Guido Berger, André Grandoni, Fabrizio
Copyright Year	2009
Abstract	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.
Ending Page	372
Page Count	18
Starting Page	355
File Format	PDF
ISSN	00255610
e-ISSN	14364646
Journal	Mathematical Programming
Issue Number	1-2
Volume Number	128
Language	English
Publisher	Springer-Verlag
Publisher Date	2009-10-13
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Matroids, geometric lattices Theoretical, Mathematical and Computational Physics Matroid intersection Combinatorial optimization Matching Factorization, matching, partitioning, covering and packing Mathematical Methods in Physics Lagrangian relaxation Mathematics of Computing Calculus of Variations and Optimal Control; Optimization Numerical Analysis Budgeted optimization Combinatorics
Content Type	Text
Resource Type	Article
Subject	Mathematics Software

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