Well solvable cases of the quadratic assignment problem with monotone and bimonotone matrices

Journal of Mathematical Modelling and Algorithms

Volumn 5, Issue 2, 2006, Pages 167-187

  Demidenko, Vitali M ^a   Finke, Gerd ^b   Gordon, Valery S ^c  

^a INSTITUTE OF MATHEMATICS   (Belarus)

^b UNIV GRENOBLE ALPES   (France)

^c UNITED INSTITUTE OF INFORMATICS PROBLEMS   (Belarus)

Author keywords

Anti Monge matrices; Quadratic assignment problem; Toeplitz matrices; Well solvable special cases

Indexed keywords

EID: 33646883684     PISSN: 15701166     EISSN: 15729214     Source Type: Journal    
DOI: 10.1007/s10852-005-9013-2     Document Type: Conference Paper

References (17)

1. Burkard, R. E., Çela, E., Demidenko, V. M., Metelski, N. N. and Woeginger, G.: Perspectives of easy and hard cases of the quadratic assignment problem. SFB Report 104, Institute of Mathematics, Technical University Graz, Austria, 1997.
2. Burkard, R. E., Çela, E., Demidenko, V. M., Metelski, N. N. and Woeginger, G.: A unified approach to simple special cases of extremal permutation problems, Optimization 44 (1998), 123-138.
3. Burkard, R. E., Çela, E., Rote, G. and Woeginger, G.: The quadratic assignment problem with an Anti-Monge and a Toeplitz matrix: easy and hard cases, Math. Program. 82 (1998), 125-158.
4. Burkov, V. C., Rubinstein, M. I. and Sokolov, V. B.: Some problems in optimal allocation of large volume memories, Avtom. Telemeh. 9 (1969), 83-91 (in Russian).
5. Cela, E. and Woeginger, G. J.: A note on the maximum of a certain bilinear form. SFB Report 8, Institute of Mathematics, Technical University Graz, Austria, 1994.
6. Demidenko, V. M.: Generalization of the strong solvability conditions of the quadratic assignment problem with Anti-Monge and Toeplitz matrices, Dokl. Nac. Akad. Nauk Belarusi 2(2003), 15-18 (in Russian).
7. Demidenko, V. M.: Quadratic assignment problem with additively monotone and incomplete Anti-Monge matrices: conditions of well solvability, Diskretn. Mat, (submitted, in Russian).
8. Finke, G., Burkard, R. E. and Rendl, F.: The quadratic assignment problem, Ann. Discrete Math. 31 (1987), 61-82.
9. Hardy, G. H., Littlewood, J. E. and Pólya, G.: The maximum of a certain bilinear form, Proc. Lond. Math. Soc. 25 (1926), 265-282.
10. Hardy, G. H., Littlewood, J. E. and Pólya, G.: Inequalities, Cambridge University Press, Cambridge, 1934.
11. Koopmans, T. C. and Beckmann, M. J.: Assignment problems and the location of economic activities, Econometrica 25 (1957), 53-76.
12. Lawler, E. L.: The quadratic assignment problem: A brief review, in B. Roy (ed.), Combinatorial Programming: Methods and Applications, Reidel Publishing Company, Dordrecht, 1975, pp. 351-360.
13. Metelski, N. N.: On extremal values of quadratic forms on symmetric groups, Vesti Akademii Nauk BSSR. Ser. Fiz.-Mat. Nauk. 6 (1972), 107-110 (in Russian).
14. Pardalos, P., Rendl, F. and Wolkowicz, H.: The quadratic assignment problem: a survey and recent developments, in P. Pardalos and H. Wolkowicz (eds.), Proceedings of the DIMACS Workshop on Quadratic Assignment Problem, DIMACS Series in Discrete Mathematics 16, 1994, pp. 1-42.
15. Pratt, V. R.: An N log N algorithm to distribute N records optimally in a sequential access file, in R. E. Miller and J. W. Thatcher (eds.) Complexity of Computer Computations, Plenum, New York, 1972, pp. 111-118.
16. Timofeev, B. B. and Litvinov, V. A.: On the extremal value of a quadratic form, Kibernetika 4(1969), 56-61 (in Russian).
17. Vickson, R. G. and Lu, X.: Optimal product and server locations in one-dimensional storage racks, Eur. J. Oper. Res. 105 (1998), 18-28.