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.
Similar content being viewed by others
References
M.L. Balinski, Signature methods for the assignment problem, Oper. Res. 33(1985)527.
M.L. Balinski, A competitive (dual) simplex method for the assignment problem, Math. Progr. 34(1986)125.
R.S. Barr, F. Glover and D. Klingman, The alternating basis algorithm for assignment problems, Math. Progr. 13(1977)1.
D.P. Bertsekas, A new algorithm for the assignment problem, Math. Progr. 21(1981)152.
F. Bourgeois and J.C. Lassalle, Algorithm 415; algorithm for the assignment problem (rectangular matrices), Comm. ACM 14(1971)805.
R.E. Burkard and U. Derigs,Assignment and Matching Problems: Solution Methods with FORTRAN-Programs (Springer Verlag, Berlin, 1980).
G. Carpaneto and P. Toth, Algorithm 548; solution of the assignment problem, ACM Trans. on Math. Software 6(1980)104.
G. Carpaneto and P. Toth, Algorithm for the solution of the assignment problem for sparse matrices, Computing 31(1983)83.
G. Carpaneto, S. Martello and P. Toth,The Assignment Problem: Methods and Algorithms (SOFMAT, CNR Italy, 1984) (in Italian).
P. Carraresi and C. Sodini, An efficient algorithm for the bipartite matching problem, Eur. J. Oper. Res. 23(1986)86.
J. Edmonds and R.M. Karp, Theoretical improvements in algorithmic efficiency of network flow problems, J. ACM 19(1972)248.
L.R. Ford, Jr. and D.R. Fulkerson,Flows in Networks (Princeton University Press, Princeton, 1962).
D. Goldfarb, Efficient dual simplex algorithms for the assignment problem, Math. Progr. 33(1985)187.
N.W. Kuhn, The Hungarian method for the assignment problem, Naval Res. Logist. Quart. 2(1955)83.
N.W. Kuhn, Variants of the Hungarian method for the assignment problem, Naval Res. Logist. Quart. 3(1956)253.
E.L. Lawler,Combinatorial Optimization: Networks and Matroids (Holt, Rinehart and Winston, New York, 1976).
R.E. Machol and M. Wien, A hard assignment problem, Oper. Res. 24(1976)190.
R.E. Machol and M. Wien, Errata to “A hard assignment problem”, Oper. Res. 25(1977)364.
L.F. McGinnis, Implementation and testing of a primal-dual algorithm for the assignment problem, Oper. Res. 31(1983)277.
B.G. Ryder and A.D. Hall, The PFORT verifier, Computing Science Technical Report No. 12, Bell Laboratories, Murray Hill, New Jersey (1981).
R. Silver, An algorithm for the assignment problem, Comm. ACM 3(1960)605.
N. Tomizawa, On some techniques useful for solution of transportation network problems, Networks 1(1971)173.
Author information
Authors and Affiliations
Additional information
Research supported by C.N.R., Progetto Finalizzato Informatica-SOFMAT, Italy.
Rights 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
Issue Date:
DOI: https://doi.org/10.1007/BF02288323