Linearizable special cases of the QAP
- 170 Downloads
We consider special cases of the quadratic assignment problem (QAP) that are linearizable in the sense of Bookhold. We provide combinatorial characterizations of the linearizable instances of the weighted feedback arc set QAP, and of the linearizable instances of the traveling salesman QAP. As a by-product, this yields a new well-solvable special case of the weighted feedback arc set problem.
KeywordsCombinatorial optimization Quadratic assignment problem Linear assignment problem Computational complexity
Part of this research was conducted while Vladimir Deineko and Gerhard Woeginger were visiting TU Graz, and they both thank the Austrian Science Fund (FWF): W1230, Doctoral Program in “Discrete Mathematics” for the financial support. Vladimir Deineko acknowledges support by Warwick University’s Centre for Discrete Mathematics and Its Applications (DIMAP). Gerhard Woeginger acknowledges support by DIAMANT (a mathematics cluster of the Netherlands Organization for Scientific Research NWO).
- Erdogan G (2006) Quadratic assignment problem: linearizations and polynomial time solvable cases. Ph.D. Thesis, Bilkent UniversityGoogle Scholar
- Festa P, Pardalos PM, Resende MGC (2000) Feedback set problems. In: Du DZ, Pardalos PM (eds) Handbook of combinatorial optimization, supplement. Kluwer Academic Publishers, Philip Drive Norwell, pp 209–259Google Scholar
- Gabovich E (1976) Constant discrete programming problems on substitute sets (in Russian). Kibernetika (Kiev) 5:128–134 English tranlation inCybernetics 12:786–793 (1977)Google Scholar
- Gilmore PC, Lawler EL, Shmoys DB (1985) Well-solved special cases. In: Lawler EL, Lenstra JK, Rinnooy Kan AHG, Shmoys DB (eds) The traveling salesman problem, vol 4. Wiley, Chichester, pp 87–143Google Scholar