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. © 2009 Springer and Mathematical Programming Society.

Berger, A., Bonifaci, V., Grandoni, F., & Schafer, G. (2011). Budgeted matching and budgeted matroid intersection via the gasoline puzzle. MATHEMATICAL PROGRAMMING, 128(1-2), 355-372 [10.1007/s10107-009-0307-4].

Budgeted matching and budgeted matroid intersection via the gasoline puzzle

Bonifaci V.
;
2011

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. © 2009 Springer and Mathematical Programming Society.
Berger, A., Bonifaci, V., Grandoni, F., & Schafer, G. (2011). Budgeted matching and budgeted matroid intersection via the gasoline puzzle. MATHEMATICAL PROGRAMMING, 128(1-2), 355-372 [10.1007/s10107-009-0307-4].
File in questo prodotto:
File Dimensione Formato  
budget-mp.pdf

accesso aperto

Tipologia: Documento in Pre-print
Licenza: DRM non definito
Dimensione 209.48 kB
Formato Adobe PDF
209.48 kB Adobe PDF Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11590/381271
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 35
  • ???jsp.display-item.citation.isi??? 23
social impact