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Budgeted Matching and Budgeted Matroid Intersection via the Gasoline Puzzle

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Budgeted Matching and Budgeted Matroid Intersection via the Gasoline Puzzle. / Berger, A.; Bonifaci, V.; Grandoni, F.; Schäfer, G.

In: Mathematical Programming, Vol. 128, No. 1-2, 06.2011, p. 355-372.

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Berger, A. ; Bonifaci, V. ; Grandoni, F. ; Schäfer, G. / Budgeted Matching and Budgeted Matroid Intersection via the Gasoline Puzzle. In: Mathematical Programming. 2011 ; Vol. 128, No. 1-2. pp. 355-372.

Bibtex

@article{9374854b643c4933968134bc6bb8ed87,
title = "Budgeted Matching and Budgeted Matroid Intersection via the Gasoline Puzzle",
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.",
keywords = "Matching, Matroid intersection, Budgeted optimization, Lagrangian relaxation, TREE, ALGORITHMS",
author = "A. Berger and V. Bonifaci and F. Grandoni and G. Sch{\"a}fer",
year = "2011",
month = "6",
doi = "10.1007/s10107-009-0307-4",
language = "English",
volume = "128",
pages = "355--372",
journal = "Mathematical Programming",
issn = "0025-5610",
publisher = "Springer Verlag",
number = "1-2",

}

RIS

TY - JOUR

T1 - Budgeted Matching and Budgeted Matroid Intersection via the Gasoline Puzzle

AU - Berger, A.

AU - Bonifaci, V.

AU - Grandoni, F.

AU - Schäfer, G.

PY - 2011/6

Y1 - 2011/6

N2 - 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.

AB - 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.

KW - Matching

KW - Matroid intersection

KW - Budgeted optimization

KW - Lagrangian relaxation

KW - TREE

KW - ALGORITHMS

U2 - 10.1007/s10107-009-0307-4

DO - 10.1007/s10107-009-0307-4

M3 - Article

VL - 128

SP - 355

EP - 372

JO - Mathematical Programming

T2 - Mathematical Programming

JF - Mathematical Programming

SN - 0025-5610

IS - 1-2

ER -