Advertisement

Assignment problems: Recent solution methods and applications

  • Rainer E. Burkard
Conference paper
Part of the Lecture Notes in Control and Information Sciences book series (LNCIS, volume 84)

Abstract

Recent developments for linear and quadratic assignment problems are surveyed. In particular some new efficient solution techniques are outlined and a recent application concerning the assignment of time-slots in a time division multiple access system is described. Finally assignment problems are used to solve a problem in channel routing.

Keywords

Assignment Problem Switch Mode Quadratic Assignment Problem Data Burst Hungarian Method 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. M.J. AATALLAH and S.E. HAMBRUSH (1984), On terminal assignments that minimize the density. Techn.Report CSD-TR-468, Purdue Univ., West Lafayette (Indiana), USA.Google Scholar
  2. M.J. ATALLAH and S.E. HAMBRUSH (1985), An assignment algorithm with applications to layout design. Techn.Report, Purdue Univ., West Lafayette (Indiana), USA.Google Scholar
  3. D.P. BERTSEKAS (1981), A new algorithm for the assignment problem. Mathematical Programming 21, 152–171.Google Scholar
  4. G. BIRKHOFF (1944), Tres observaciones sobre el algebra lineal. Rev.univ.nac.Tucumán (Ser.A) 5, 147–151.Google Scholar
  5. V.Y.BURDYUK and V.N.TROFIMOV (1976), Generalization of the results of Gilmore and Gomory on the solution of the traveling salesman problem. Izv.Akad.Nauk SSSR, Techn.Kibernet.3, 16–22 (Russian); translated as Eng.Cybernetics 14 (1976), 12–18.Google Scholar
  6. R.E.BURKARD (1983), Locations with spatial interactions — the quadratic assignment problem. Report 83-31, Math.Institut, Techn.Universität Graz. To appear in R.L.Francis and P.B.Mirchandani (Eds.): Discrete Location Theory, Academic Press, 1986.Google Scholar
  7. R.E. BURKARD (1984), Quadratic assignment problems. European J. of Operational Research 15, 283–289.Google Scholar
  8. R.E. BURKARD (1985), Time-slot assignments for TDMA-systems. Computing 35, 99–112.Google Scholar
  9. R.E.BURKARD and U.DERIGS (1980), Assignment and Matching Problems: Solution Methods with FORTRAN-programs. Springer (LN Econ. and Math.Systems, Vol.184), Berlin-Heidelberg-New York.Google Scholar
  10. R.E. BURKARD and U. FINCKE (1982), On random quadratic bottleneck problems. Mathematical Programming 23, 227–232.Google Scholar
  11. R.E. BURKARD and U. FINCKE (1983), The asymptotic probabilistic behaviour of quadratic sum assignment problems. Zeitschrift für Operations Research, Ser.A 27, 73–81.Google Scholar
  12. R.E. BURKARD and U. FINCKE (1985), Probabilistic asymptotic properties of some combinatorial optimization problems. Discrete Applied Maths. 12, 21–29.Google Scholar
  13. R.E. BURKARD, W. HAHN and U. ZIMMERMANN (1977), An algebraic approach to assignment problems. Mathematical Programming 12, 318–327.Google Scholar
  14. R.E. BURKARD and F. RENDL (1984), A thermodynamically motivated simulation procedure for combinatorial optimization problems. European J. of Operational Research 17, 169–174.Google Scholar
  15. R.E. BURKARD and U. ZIMMERMANN (1980), Weakly admissible transformations for solving algebraic assignment and transportation problems. Math.Programming Study 12, 1–18.Google Scholar
  16. G. CARPANETO and P. TOTH (1980), Algorithm 548 (Solution of the assignment problem). ACM Trans. on Math.Software 6, 104–111Google Scholar
  17. G. CARPANETO and P. TOTH (1981), Algorithm 44: Algorithm for the solution of the bottle-neck assignment problem. Computing 27, 179–187.Google Scholar
  18. G. CARPANETO and P. TOTH (1983), Algorithm 50: Algorithm for the solution of the assignment problem for sparse matrices. Computing 31, 83–94.Google Scholar
  19. W.M. CUNNINGHAM and A.B. MARSH, III (1978), A primal algorithm for optimum matching. Mathematical Programming Study 8, 50–72.Google Scholar
  20. V.G. DEINEKO and V.L. FILONENKO (1979), On the reconstruction of specially structured matrices. In: Aktualnye problemy EVM; programmirovanie. Dnepropetrovsk: DGU, 43–45 (Russian).Google Scholar
  21. U. DERIGS and A. METZ (1985), An in-core/out of core method for solving large scale assignment problems. Report No. 85376-OR, Institut für Operations Research, Universität Bonn, F.R.G.Google Scholar
  22. M.E. DYER, A.M. FRIEZE and C.J.H. McDIARMID (1984), Partitioning heuristics for two geometric maximization problems. Operations Research Letters 3, 267–270.Google Scholar
  23. G.FINKE, R.E.BURKARD and F.RENDL (1986), Quadratic assignment problems. To appear in: Annals of Discrete Maths., 1986.Google Scholar
  24. B. GAVISH, P. SCHWEITZER and E. SHLIFER (1977), The zero pivot phenomenon in transportation and assignment problems and its computational implications. Mathematical Programming 12, 226–240.Google Scholar
  25. P.C. GILMORE and R.E. GOMORY (1964), Sequencing a one-state variable machine: a solvable case of the traveling salesman problem. Operations Research 12, 655–679.Google Scholar
  26. D. GOLDFARB (1985), Efficient dual simplex algorithms for the assignment problem. Mathematical Programming 33, 187–203.Google Scholar
  27. Ph. HALL (1935), On representations of subsets. J.London Math.Soc. 10, 26–30.Google Scholar
  28. A.J.HOFFMAN (1963), On simple linear programming problems. Proc. of Symp. on Pure Maths., VII, Convexity, AMS, 317–327.Google Scholar
  29. J.E. HOPCROFT and R.M. KARP (1973), An n5/2 algorithm for maximum matchings in bipartite graphs. SIAM J.Comput. 2, 225–231.Google Scholar
  30. M. IRI, K. MUROTA and Sh. MATSUI (1983), Heuristics for planar minimum-weight perfect matchings. Networks 13, 67–92.Google Scholar
  31. R.M. KARP and S.R. LI (1975), Two special cases of the assignment problem. Discrete Maths. 13, 129–142.Google Scholar
  32. H.W. KUHN (1955), The Hungarian method for assignment problems. Nav.Res.Log.Quart. 2, 83–97.Google Scholar
  33. S. MARTELLO, W.R. PULLEYBLANK, P. TOTH and D. deWERRA (1984), Balanced optimization problems. Operations Research Letters 3, 275–278.Google Scholar
  34. C.H.PAPADIMITRIOU (1977), The probabilistic analysis of matching algorithms. Proc. 15th Ann. Allerton Conf. on Communication, Control and Computing, 368–378.Google Scholar
  35. G.L. THOMPSON (1981), A recursive method for solving assignment problems. In: P. Hansen (Ed.): Studies on Graphs and Discrete Programming, 319–343 (Annals of Discrete Mathematics, Vol.11), North Holland: Amsterdam-New York-Oxford.Google Scholar
  36. N. TOMIZAWA (1971), On some techniques useful for solution of transportation network problems. Networks 1, 173–194.Google Scholar
  37. D.W. WALKUP (1979), On the expected value of random assignment problems. SIAM J.Comput. 8, 440–442.Google Scholar
  38. M. WEBER and Th.M. LIEBLING (1985), Euclidean matching problems and the Metropolis algorithm. Report, Département de Mathématiques, EPF-Lausanne, Switzerland.Google Scholar

Copyright information

© Springer-Verlag 1986

Authors and Affiliations

  • Rainer E. Burkard
    • 1
  1. 1.Technische Universität Graz Institut für MathematikGrazAustria

Personalised recommendations