Given a graph G where a label is associated with each edge, we address the problem of looking for a maximum matching of G using the minimum number of different labels, namely the labeled maximum matching problem. It is a relatively new problem whose application is related to the timetabling problem. We prove it is NP-complete and present four different mathematical formulations. Moreover, we propose an exact algorithm based on a branch-and-bound approach to solve it. We evaluate the performance of our algorithm on a wide set of instances and compare our computational times with the ones required by CPLEX to solve the proposed mathematical formulations. Test results show the effectiveness of our procedure, that hugely outperforms the solver.

The Labeled Maximum Matching Problem

CARRABS, FRANCESCO
;
CERULLI, Raffaele;GENTILI, Monica
2009-01-01

Abstract

Given a graph G where a label is associated with each edge, we address the problem of looking for a maximum matching of G using the minimum number of different labels, namely the labeled maximum matching problem. It is a relatively new problem whose application is related to the timetabling problem. We prove it is NP-complete and present four different mathematical formulations. Moreover, we propose an exact algorithm based on a branch-and-bound approach to solve it. We evaluate the performance of our algorithm on a wide set of instances and compare our computational times with the ones required by CPLEX to solve the proposed mathematical formulations. Test results show the effectiveness of our procedure, that hugely outperforms the solver.
File in questo prodotto:
Non ci sono file associati a questo prodotto.

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: https://hdl.handle.net/11386/1993152
 Attenzione

Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo

Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 22
  • ???jsp.display-item.citation.isi??? 16
social impact