Skip to main content
Log in

Algorithms and codes for the assignment problem

  • Chapter III Assignment And Matching
  • Published:
Annals of Operations Research Aims and scope Submit manuscript

Abstract

This paper analyzes the most efficient algorithms for the Linear Min-Sum Assignment Problem and shows that they derive from a common basic procedure. For each algorithm, we evaluate the computational complexity and the average performance on randomly-generated test problems. Efficient FORTRAN implementations for the case of complete and sparse matrices are given.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. M.L. Balinski, Signature methods for the assignment problem, Oper. Res. 33(1985)527.

    Google Scholar 

  2. M.L. Balinski, A competitive (dual) simplex method for the assignment problem, Math. Progr. 34(1986)125.

    Google Scholar 

  3. R.S. Barr, F. Glover and D. Klingman, The alternating basis algorithm for assignment problems, Math. Progr. 13(1977)1.

    Google Scholar 

  4. D.P. Bertsekas, A new algorithm for the assignment problem, Math. Progr. 21(1981)152.

    Google Scholar 

  5. F. Bourgeois and J.C. Lassalle, Algorithm 415; algorithm for the assignment problem (rectangular matrices), Comm. ACM 14(1971)805.

    Google Scholar 

  6. R.E. Burkard and U. Derigs,Assignment and Matching Problems: Solution Methods with FORTRAN-Programs (Springer Verlag, Berlin, 1980).

    Google Scholar 

  7. G. Carpaneto and P. Toth, Algorithm 548; solution of the assignment problem, ACM Trans. on Math. Software 6(1980)104.

    Google Scholar 

  8. G. Carpaneto and P. Toth, Algorithm for the solution of the assignment problem for sparse matrices, Computing 31(1983)83.

    Google Scholar 

  9. G. Carpaneto, S. Martello and P. Toth,The Assignment Problem: Methods and Algorithms (SOFMAT, CNR Italy, 1984) (in Italian).

  10. P. Carraresi and C. Sodini, An efficient algorithm for the bipartite matching problem, Eur. J. Oper. Res. 23(1986)86.

    Google Scholar 

  11. J. Edmonds and R.M. Karp, Theoretical improvements in algorithmic efficiency of network flow problems, J. ACM 19(1972)248.

    Google Scholar 

  12. L.R. Ford, Jr. and D.R. Fulkerson,Flows in Networks (Princeton University Press, Princeton, 1962).

    Google Scholar 

  13. D. Goldfarb, Efficient dual simplex algorithms for the assignment problem, Math. Progr. 33(1985)187.

    Google Scholar 

  14. N.W. Kuhn, The Hungarian method for the assignment problem, Naval Res. Logist. Quart. 2(1955)83.

    Google Scholar 

  15. N.W. Kuhn, Variants of the Hungarian method for the assignment problem, Naval Res. Logist. Quart. 3(1956)253.

    Google Scholar 

  16. E.L. Lawler,Combinatorial Optimization: Networks and Matroids (Holt, Rinehart and Winston, New York, 1976).

    Google Scholar 

  17. R.E. Machol and M. Wien, A hard assignment problem, Oper. Res. 24(1976)190.

    Google Scholar 

  18. R.E. Machol and M. Wien, Errata to “A hard assignment problem”, Oper. Res. 25(1977)364.

    Google Scholar 

  19. L.F. McGinnis, Implementation and testing of a primal-dual algorithm for the assignment problem, Oper. Res. 31(1983)277.

    Google Scholar 

  20. B.G. Ryder and A.D. Hall, The PFORT verifier, Computing Science Technical Report No. 12, Bell Laboratories, Murray Hill, New Jersey (1981).

    Google Scholar 

  21. R. Silver, An algorithm for the assignment problem, Comm. ACM 3(1960)605.

    Google Scholar 

  22. N. Tomizawa, On some techniques useful for solution of transportation network problems, Networks 1(1971)173.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Research supported by C.N.R., Progetto Finalizzato Informatica-SOFMAT, Italy.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Carpaneto, G., Martello, S. & Toth, P. Algorithms and codes for the assignment problem. Ann Oper Res 13, 191–223 (1988). https://doi.org/10.1007/BF02288323

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02288323

Keywords

Navigation