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Volumn 100, Issue 1-2, 2000, Pages 17-48

Algorithms and codes for dense assignment problems: The state of the art

Author keywords

Comparison of algorithms; Dense matrices; Experimental evaluation; Linear assignment problem

Indexed keywords


EID: 0347306743     PISSN: 0166218X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0166-218X(99)00172-9     Document Type: Article
Times cited : (85)

References (55)
  • 1
    • 0002706294 scopus 로고
    • The scaling network simplex algorithm
    • Ahuja R.K., Orlin J.B. The scaling network simplex algorithm. Oper. Res. (Suppl. 1):1992;S5-S13.
    • (1992) Oper. Res. , vol.1
    • Ahuja, R.K.1    Orlin, J.B.2
  • 2
    • 0024032520 scopus 로고
    • A sequential dual simplex algorithm for the linear assignment problem
    • Akgül M. A sequential dual simplex algorithm for the linear assignment problem. Oper. Res. Lett. 7:1988;155-158.
    • (1988) Oper. Res. Lett. , vol.7 , pp. 155-158
    • Akgül, M.1
  • 3
    • 38249023196 scopus 로고
    • Erratum. a sequential dual simplex algorithm for the linear assignment problem
    • Akgül M. Erratum. A sequential dual simplex algorithm for the linear assignment problem. Oper. Res. Lett. 8:1989;117.
    • (1989) Oper. Res. Lett. , vol.8 , pp. 117
    • Akgül, M.1
  • 4
    • 25344442966 scopus 로고
    • The linear assignment problem
    • in: M. Akgül, H.W. Hamacher, S. Tüfekçi (Eds.), Springer, Berlin
    • M. Akgül, The linear assignment problem, in: M. Akgül, H.W. Hamacher, S. Tüfekçi (Eds.), Combinatorial Optimization NATO ASI Series F, vol. 82, Springer, Berlin, 1992, pp. 85-122.
    • (1992) Combinatorial Optimization NATO ASI Series F , vol.82 , pp. 85-122
    • Akgül, M.1
  • 5
    • 38249000277 scopus 로고
    • A genuinely polynomial primal simplex algorithm for the assignment problem
    • Akgül M. A genuinely polynomial primal simplex algorithm for the assignment problem. Discr. Appl. Math. 45:1993;93-115.
    • (1993) Discr. Appl. Math. , vol.45 , pp. 93-115
    • Akgül, M.1
  • 6
    • 0003875064 scopus 로고
    • Computational results with a branch and cut code for the capacitated vehicle routing problem
    • IMAG, Grenoble, France
    • P. Augerat, J.M. Belenguer, E. Benavent, A. Corberán, D. Naddef, G. Rinaldi, Computational results with a branch and cut code for the capacitated vehicle routing problem, Tech. Rep. RR949-M, IMAG, Grenoble, France, 1995.
    • (1995) Tech. Rep. RR949-M
    • Augerat, P.1    Belenguer, J.M.2    Benavent, E.3    Corberán, A.4    Naddef, D.5    Rinaldi, G.6
  • 7
    • 0000620444 scopus 로고
    • A parallel augmenting shortest path algorithm for the assignment problem
    • Balas E., Miller D., Pekny J., Toth P. A parallel augmenting shortest path algorithm for the assignment problem. J. ACM. 38:1991;985-1004.
    • (1991) J. ACM , vol.38 , pp. 985-1004
    • Balas, E.1    Miller, D.2    Pekny, J.3    Toth, P.4
  • 8
    • 0021518518 scopus 로고
    • The Hirsch conjecture for dual transportation polyhedra
    • Balinski M.L. The Hirsch conjecture for dual transportation polyhedra. Math. Oper. Res. 9:1984;629-633.
    • (1984) Math. Oper. Res. , vol.9 , pp. 629-633
    • Balinski, M.L.1
  • 9
    • 0022061479 scopus 로고
    • Signature methods for the assignment problem
    • Balinski M.L. Signature methods for the assignment problem. Oper. Res. 33:1985;527-536.
    • (1985) Oper. Res. , vol.33 , pp. 527-536
    • Balinski, M.L.1
  • 10
    • 0022676208 scopus 로고
    • A competitive (dual) simplex method for the assignment problem
    • Balinski M.L. A competitive (dual) simplex method for the assignment problem. Math. Program. 34:1986;125-141.
    • (1986) Math. Program. , vol.34 , pp. 125-141
    • Balinski, M.L.1
  • 11
    • 0002224079 scopus 로고
    • The alternating basis algorithm for assignment problems
    • Barr R.S., Glover F., Klingman D. The alternating basis algorithm for assignment problems. Math. Program. 13:1977;1-13.
    • (1977) Math. Program , vol.13 , pp. 1-13
    • Barr, R.S.1    Glover, F.2    Klingman, D.3
  • 12
    • 0025384023 scopus 로고
    • Linear programming on Cray supercomputers
    • Beasley J.E. Linear programming on Cray supercomputers. J. Oper. Res. Soc. 41:1990;133-139.
    • (1990) J. Oper. Res. Soc. , vol.41 , pp. 133-139
    • Beasley, J.E.1
  • 13
    • 56449107505 scopus 로고
    • Or-library: Distributing test problems by electronic mail
    • Beasley J.E. Or-library: distributing test problems by electronic mail. J. Oper. Res. Soc. 41:1990;1069-1072.
    • (1990) J. Oper. Res. Soc. , vol.41 , pp. 1069-1072
    • Beasley, J.E.1
  • 14
    • 34250244023 scopus 로고
    • A new algorithm for the assignment problem
    • Bertsekas D.P. A new algorithm for the assignment problem. Math. Program. 21:1981;152-171.
    • (1981) Math. Program. , vol.21 , pp. 152-171
    • Bertsekas, D.P.1
  • 16
    • 34250089474 scopus 로고
    • Dual coordinate step methods for linear network flow problems
    • Bertsekas D.P., Eckstein J. Dual coordinate step methods for linear network flow problems. Math. Program. 42:1988;203-243.
    • (1988) Math. Program. , vol.42 , pp. 203-243
    • Bertsekas, D.P.1    Eckstein, J.2
  • 17
    • 0026226724 scopus 로고
    • Parallel synchronous and asynchronous implementations of the auction algorithm
    • Bertsekas D.P., Castañon D.A. Parallel synchronous and asynchronous implementations of the auction algorithm. Parallel Comput. 17:1991;707-732.
    • (1991) Parallel Comput. , vol.17 , pp. 707-732
    • Bertsekas, D.P.1    Castañon, D.A.2
  • 19
    • 0346691854 scopus 로고    scopus 로고
    • Linear assignment and extensions
    • Institut für Mathematik, Technische Universität Graz
    • R.E. Burkard, U. Derigs, Assignment and Matching Problems: Solution Methods with FORTRAN Programs, Springer, Berlin, 1980. R.E. Burkard, E. Cela, Linear assignment and extensions, Tech. Rep. 127, Institut für Mathematik, Technische Universität Graz (1998) .
    • (1998) Tech. Rep. 127
    • Burkard, R.E.1    Cela, E.2
  • 20
    • 0000291844 scopus 로고
    • Exact solution of large-scale, asymmetric traveling salesman problems
    • Carpaneto G., Dell'Amico M., Toth P. Exact solution of large-scale, asymmetric traveling salesman problems. ACM Trans. Math. Software. 21:1995;394-409.
    • (1995) ACM Trans. Math. Software , vol.21 , pp. 394-409
    • Carpaneto, G.1    Dell'Amico, M.2    Toth, P.3
  • 21
    • 34250097087 scopus 로고
    • Algorithms and codes for the assignment problem
    • in: B. Simeone, P. Toth, G. Gallo, F. Maffioli, S. Pallottino (Eds.), Fortran Codes for Network Optimization Baltzer, Basel
    • G. Carpaneto, S. Martello, P. Toth, Algorithms and codes for the assignment problem, in: B. Simeone, P. Toth, G. Gallo, F. Maffioli, S. Pallottino (Eds.), Fortran Codes for Network Optimization, Ann. Oper. Res., Vol. 13, Baltzer, Basel, 1988, pp. 193-223.
    • (1988) Ann. Oper. Res. , vol.13 , pp. 193-223
    • Carpaneto, G.1    Martello, S.2    Toth, P.3
  • 23
    • 0022153170 scopus 로고
    • Primal-dual algorithms for the assignment problem
    • Carpaneto G., Toth P. Primal-dual algorithms for the assignment problem. Discrete Appl. Math. 18:1987;137-153.
    • (1987) Discrete Appl. Math. , vol.18 , pp. 137-153
    • Carpaneto, G.1    Toth, P.2
  • 24
    • 0347952768 scopus 로고
    • Reverse auction algorithms for assignment problems
    • in: D.S. Johnson, C.C. McGeoch (Eds.), American Mathematical Society, Providence, RI
    • D.A. Castañon, Reverse auction algorithms for assignment problems, in: D.S. Johnson, C.C. McGeoch (Eds.), Network Flows and Matching: First DIMACS Implementation Challenge, American Mathematical Society, Providence, RI, 1993, pp. 407-430.
    • (1993) Network Flows and Matching: First DIMACS Implementation Challenge , pp. 407-430
    • Castañon, D.A.1
  • 25
    • 0001549833 scopus 로고
    • An Algorithm for the vehicle dispatching problem
    • Christofides N., Eilon S. An Algorithm for the vehicle dispatching problem. Oper. Res. Quart. 20:1969;309-318.
    • (1969) Oper. Res. Quart. , vol.20 , pp. 309-318
    • Christofides, N.1    Eilon, S.2
  • 26
    • 0001208905 scopus 로고
    • The vehicle routing problem
    • in: N. Christofides, A. Mingozzi, P. Toth, C. Sandi (Eds.), Wiley, Chichester
    • N. Christofides, A. Mingozzi, P. Toth, The vehicle routing problem, in: N. Christofides, A. Mingozzi, P. Toth, C. Sandi (Eds.), Combinatorial Optimization, Wiley, Chichester, 1979, pp. 318-338.
    • (1979) Combinatorial Optimization , pp. 318-338
    • Christofides, N.1    Mingozzi, A.2    Toth, P.3
  • 27
    • 34250381328 scopus 로고
    • A network simplex method
    • Cunningham W.H. A network simplex method. Math. Program. 11:1976;105-116.
    • (1976) Math. Program. , vol.11 , pp. 105-116
    • Cunningham, W.H.1
  • 28
    • 0027284618 scopus 로고
    • Heuristic algorithms for the multiple depot vehicle scheduling problem
    • Dell'Amico M., Fischetti M., Toth P. Heuristic algorithms for the multiple depot vehicle scheduling problem. Manage. Sci. 39:1993;115-125.
    • (1993) Manage. Sci. , vol.39 , pp. 115-125
    • Dell'Amico, M.1    Fischetti, M.2    Toth, P.3
  • 30
    • 9644260215 scopus 로고
    • The shortest augmenting path method for solving assignment problems - Motivation and computational experience
    • in: C.L. Monma, (Ed.), Algorithms and Software for Optimization - Part I, Baltzer, Basel
    • U. Derigs, The shortest augmenting path method for solving assignment problems - motivation and computational experience, in: C.L. Monma, (Ed.), Algorithms and Software for Optimization - Part I, Ann. Oper. Res., Vol. 4, Baltzer, Basel, 1985, pp. 57-102.
    • (1985) Ann. Oper. Res. , vol.4 , pp. 57-102
    • Derigs, U.1
  • 31
    • 0028461566 scopus 로고
    • Optimal solution of vehicle routing problem using minimum k-trees
    • Fisher M. Optimal solution of vehicle routing problem using minimum. k -trees Oper. Res. 42(4):1994;626-642.
    • (1994) Oper. Res. , vol.42 , Issue.4 , pp. 626-642
    • Fisher, M.1
  • 32
    • 0029204225 scopus 로고
    • An efficient cost scaling algorithm for the assignment problem
    • Goldberg A.V., Kennedy R. An efficient cost scaling algorithm for the assignment problem. Math. Program. 71:1995;153-177.
    • (1995) Math. Program. , vol.71 , pp. 153-177
    • Goldberg, A.V.1    Kennedy, R.2
  • 33
    • 38249007265 scopus 로고
    • Sublinear-time parallel algorithms for matching and related problemst
    • Goldberg A.V., Plotkin S.A., Vaidya P. Sublinear-time parallel algorithms for matching and related problemst. J. Algorithms. 14:1993;180-213.
    • (1993) J. Algorithms , vol.14 , pp. 180-213
    • Goldberg, A.V.1    Plotkin, S.A.2    Vaidya, P.3
  • 34
    • 0001764412 scopus 로고
    • Finding minimum-cost circulation by successive approximation
    • Goldberg A.V., Tarjan R.E. Finding minimum-cost circulation by successive approximation. Math. Oper. Res. 15:1990;430-466.
    • (1990) Math. Oper. Res. , vol.15 , pp. 430-466
    • Goldberg, A.V.1    Tarjan, R.E.2
  • 35
    • 0039710389 scopus 로고
    • A polynomial simplex method for the assignment problem
    • Hung M.S. A polynomial simplex method for the assignment problem. Oper. Res. 31:1983;595-600.
    • (1983) Oper. Res. , vol.31 , pp. 595-600
    • Hung, M.S.1
  • 37
    • 0022795790 scopus 로고
    • Improving the Hungarian assignment algorithm
    • Jonker R., Volgenant A. Improving the Hungarian assignment algorithm. Oper. Res. Lett. 5:1986;171-175.
    • (1986) Oper. Res. Lett. , vol.5 , pp. 171-175
    • Jonker, R.1    Volgenant, A.2
  • 38
    • 0023173192 scopus 로고
    • A shortest augmenting path algorithm for dense and sparse linear assignment problems
    • Jonker R., Volgenant A. A shortest augmenting path algorithm for dense and sparse linear assignment problems. Computing. 38:1987;325-340.
    • (1987) Computing , vol.38 , pp. 325-340
    • Jonker, R.1    Volgenant, A.2
  • 39
    • 0026224123 scopus 로고
    • An empirical analysis of the dense assignment problem: Sequential and parallel implementations
    • Kennington J.L., Wang Z. An empirical analysis of the dense assignment problem: Sequential and parallel implementations. ORSA J. Comput. 3:1991;299-306.
    • (1991) ORSA J. Comput. , vol.3 , pp. 299-306
    • Kennington, J.L.1    Wang, Z.2
  • 40
    • 0002719797 scopus 로고
    • The Hungarian method for the assignment problem
    • Kuhn H.W. The Hungarian method for the assignment problem. Naval Res. Logistics Quart. 2:1955;83-97.
    • (1955) Naval Res. Logistics Quart. , vol.2 , pp. 83-97
    • Kuhn, H.W.1
  • 41
    • 0002719797 scopus 로고
    • Variants of the Hungarian method for the assignment problem
    • Kuhn H.W. Variants of The Hungarian method for the assignment problem. Naval Res. Logistics Quart. 3:1956;253-258.
    • (1956) Naval Res. Logistics Quart. , vol.3 , pp. 253-258
    • Kuhn, H.W.1
  • 43
    • 0041579189 scopus 로고
    • A hard assignment problem
    • Machol R.E., Wien M. A hard assignment problem. Oper. Res. 24:1976;190-192.
    • (1976) Oper. Res. , vol.24 , pp. 190-192
    • Machol, R.E.1    Wien, M.2
  • 45
    • 0000250164 scopus 로고
    • Linear assignment problems
    • in: S. Martello, G. Laporte, M. Minoux, C. Ribeiro, (Eds.), North-Holland, Amsterdam
    • S. Martello, P. Toth, Linear assignment problems, in: S. Martello, G. Laporte, M. Minoux, C. Ribeiro, (Eds.), Surveys in Combinatorial Optimization, Annals of Discrete. Mathematics, Vol. 31, North-Holland, Amsterdam, 1987, pp. 259-282.
    • (1987) Surveys in Combinatorial Optimization, Annals of Discrete. Mathematics , vol.31 , pp. 259-282
    • Martello, S.1    Toth, P.2
  • 46
    • 0020717996 scopus 로고
    • Implementation and testing of a primal-dual algorithm for the assignment problem
    • McGinnis L.F. Implementation and testing of a primal-dual algorithm for the assignment problem. Oper. Res. 31:1983;277-299.
    • (1983) Oper. Res. , vol.31 , pp. 277-299
    • McGinnis, L.F.1
  • 47
    • 0022134586 scopus 로고
    • On the simplex algorithm for networks and generalized networks
    • Orlin J.B. On the simplex algorithm for networks and generalized networks. Math. Program. Stud. 24:1985;166-178.
    • (1985) Math. Program. Stud. , vol.24 , pp. 166-178
    • Orlin, J.B.1
  • 48
    • 0343675970 scopus 로고
    • New scaling algorithms for the assignment and minimum cycle mean problems
    • Orlin J.B., Ahuja R.K. New scaling algorithms for the assignment and minimum cycle mean problems. Math. Program. 54:1992;41-56.
    • (1992) Math. Program. , vol.54 , pp. 41-56
    • Orlin, J.B.1    Ahuja, R.K.2
  • 50
    • 0002334145 scopus 로고
    • An approximate dual projective algorithm for solving assignment problems
    • in: D.S. Johnson, C.C. McGeoch (Eds.), American Mathematical Society, Providence, RI
    • K.G. Ramakrishnan, N.K. Karmarkar, A.P. Kamath, An approximate dual projective algorithm for solving assignment problems, in: D.S. Johnson, C.C. McGeoch (Eds.), Network Flows and Matching: First DIMACS Implementation Challenge, American Mathematical Society, Providence, RI, 1993, pp. 431-452.
    • (1993) Network Flows and Matching: First DIMACS Implementation Challenge , pp. 431-452
    • Ramakrishnan, K.G.1    Karmarkar, N.K.2    Kamath, A.P.3
  • 51
    • 0026225350 scopus 로고
    • Tsplib - A travelling salesman problem library
    • Reinelt G. Tsplib - A travelling salesman problem library. ORSA J. Comput. 4:1991;376-384.
    • (1991) ORSA J. Comput. , vol.4 , pp. 376-384
    • Reinelt, G.1
  • 52
    • 0028405634 scopus 로고
    • A computational analysis of the auction algorithm
    • Schwartz B.L. A computational analysis of the auction algorithm. European. J. Oper. Res. 42:1994;161-169.
    • (1994) European. J. Oper. Res. , vol.42 , pp. 161-169
    • Schwartz, B.L.1
  • 54
    • 0030269645 scopus 로고    scopus 로고
    • Linear and semi-assignment problems: A core oriented approach
    • Volgenant A. Linear and semi-assignment problems: a core oriented approach. Comput. Oper. Res. 23:1996;917-932.
    • (1996) Comput. Oper. Res. , vol.23 , pp. 917-932
    • Volgenant, A.1
  • 55
    • 0346691845 scopus 로고
    • A comparison of two algorithms for the assignment problem
    • Zaki H. A comparison of two algorithms for the assignment problem. Comput. Opt. Appl. 41:1995;23-45.
    • (1995) Comput. Opt. Appl. , vol.41 , pp. 23-45
    • Zaki, H.1


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