The quadratic assignment problem with a monotone anti-Monge and a symmetric Toeplitz matrix: Easy and hard cases

Mathematical Programming, Series B

Volumn 82, Issue 1-2, 1998, Pages 125-158

  Burkard, Rainer E ^a   Çela, Eranda ^a   Rote, Günter ^a   Woeginger, Gerhard J ^a  

^a GRAZ UNIVERSITY OF TECHNOLOGY   (Austria)

Author keywords

Anti Monge matrices; Polynomially solvable; Quadratic assignment; Special cases; Toeplitz matrices

Indexed keywords

EID: 0041763346     PISSN: 00255610     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF01585868     Document Type: Article

References (24)

1. S.V. Amiouny, J.J. Bartholdi III, J.H. Vande Vate, J. Zhang, Balanced loading, Operations Research 40 (1992) 238-246.
2. A.A. Bolotnikov, On the best balance of the disk with masses on its periphery, Problemi Mashinostroenia 6 (1978) 68-74 (in Russian).
3. R.E. Burkard, Locations with spatial interactions: the quadratic assignment problem, in: P.B. Mirchandani, R.L. Francis (Eds.), Discrete Location Theory, ch. 9, Wiley, New York, 1990, pp. 387-437.
4. R.E. Burkard, E. Çela, G. Rote, G.J. Woeginger, The quadratic assignment problem with an Anti-Monge and a Toeplitz matrix: easy and hard cases, Technical Report SFB-34, June 1995, 30 pages, Institut für Mathematik B, Technische Universität Graz. file://ftp.tu-graz.ac.at/pub/papers/math/ sfb34.ps.gz.
5. R.E. Burkard, B. Klinz, R. Rudolf, Perspectives of Monge properties in optimization, Discrete Applied Mathematics 70 (1996) 95-161.
6. V.N. Burkov, M.I. Rubinstein, V.B. Sokolov, Some problems in optimal allocation of large-volume memories, Avtomatika i Telemekhanika 9 (1969) 83-91 (in Russian).
7. E. Çela, G.J. Woeginger, A note on the maximum of a certain bilinear form, Technical Report SFB-8, September 1994, Institut für Mathematik B, Technische Universität Graz. file://ftp.tu-graz.ac.at/pub/ papers/math/sfb8.ps.gz.
8. J. Clausen, M. Perregård, Solving large quadratic assignment problems in parallel, Computational Optimization and Applications 8 (1997) 111-127.
9. M.R. Garey, D.S. Johnson, Computers and Intractability: A Guide to the Theory of NP-Completeness, Freeman, San Francisco, 1979.
10. G.H. Hardy, J.E. Littlewood, G. Pólya, Inequalities, Cambridge University Press, Cambridge, 1967.
11. G.H. Hardy, J.E. Littlewood, G. Pólya, The maximum of a certain bilinear form, Proceedings of the London Mathematical Society 25 (1926) 265-282.
12. T.C. Koopmans, M.J. Beckmann, Assignment problems and the location of economic activities, Econometrica 25 (1957) 53-76.
13. G. Laporte, H. Mercure, Balancing hydraulic turbine runners: a quadratic assignment problem, European Journal of Operational Research 35 (1988) 378-382.
14. E.L. Lawler, The quadratic assignment problem, Management Science 9 (1963) 586-599.
15. E.L. Lawler, The quadratic assignment problem: a brief review, in: B. Roy (Ed.), Combinatorial Programming: Methods and Applications, Reidel Dordrecht, Holland, 1975, pp. 351-360.
16. E.L. Lawler, J.K. Lenstra, A.H.G. Rinnooy Kan, D.B. Shmoys, The Traveling Salesman Problem, Wiley, Chichester, 1985.
17. N.N. Metelski, On extremal values of quadratic forms on symmetric groups, Vesti Akad. Navuk BSSR Ser. Fiz.-Mat. Navuk 6 (1972) 107-110 (in Russian).
18. J. Mosevich, Balancing hydraulic turbine runners - a discrete combinatorial optimization problem, European Journal of Operational Research 26 (1986) 202-204.
19. P. Pardalos, F. Rendl, H. Wolkowicz, The quadratic assignment problem: a survey and recent developments, in: P. Pardalos, H. Wolkowicz (Eds.), Proceedings of the DIMACS Workshop on Quadratic Assignment Problems, DIMACS Series in Discrete Mathematics and Theoretical Computer Science 16 (1994) 1-42.
20. V.R. Pratt, An N log N algorithm to distribute N records optimally in a sequential access file, in: R.E. Miller, J.W. Thatcher (Eds.), Complexity of Computer Computations, Plenum Press, New York, 1972, pp. 111-118.
21. D. Schlegel, Die Unwucht-optimale Verteilung von Turbinenschaufeln als quadratisches Zuordnungs-problem, Ph.D. Thesis, ETH Zürich, 1987.
22. Y.G. Stoyan, V.Z. Sokolovskii, S.V. Yakovlev, A method for balancing discretely distributed masses under rotation, Energomashinostroenia 2 (1982) 4-5 (in Russian).
23. F. Supnick, Extreme Hamiltonian lines, Annals of Mathematics 66 (1957) 179-201.
24. B.B. Timofeev, V.A. Litvinov, On the extremal value of a quadratic form, Kibernetika 4 (1969) 56-61 (in Russian).