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Volumn 40, Issue 1, 2006, Pages 53-73

Branch and cut based on the volume algorithm: Steiner trees in graphs and MAX-cut

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; GRAPH THEORY; LINEAR PROGRAMMING; OPERATIONS RESEARCH; OPTIMIZATION; PROBLEM SOLVING;

EID: 33746253910     PISSN: 03990559     EISSN: 28047303     Source Type: Journal    
DOI: 10.1051/ro:2006010     Document Type: Article
Times cited : (9)

References (38)
  • 1
    • 84987027598 scopus 로고
    • An integer linear programming approach to the Steiner problem in graphs
    • Y.P. Aneja, An integer linear programming approach to the Steiner problem in graphs. Networks 20 (1980) 167-178.
    • (1980) Networks , vol.20 , pp. 167-178
    • Aneja, Y.P.1
  • 3
    • 0344443734 scopus 로고    scopus 로고
    • Solving Steiner tree problems in graphs with Lagrangian relaxation
    • L. Bahiense, F. Barahona and O. Porto, Solving Steiner tree problems in graphs with Lagrangian relaxation. J. Comb. Optim. 7 (2003) 259-282.
    • (2003) J. Comb. Optim. , vol.7 , pp. 259-282
    • Bahiense, L.1    Barahona, F.2    Porto, O.3
  • 4
    • 0345275423 scopus 로고    scopus 로고
    • The volume algorithm revisited: Relation with bundle methods
    • L. Bahiense, N. Maculan and C. Sagastizábal, The volume algorithm revisited: relation with bundle methods. Math. Program. 94 (2002) 41-69.
    • (2002) Math. Program. , vol.94 , pp. 41-69
    • Bahiense, L.1    Maculan, N.2    Sagastizábal, C.3
  • 5
    • 0011302065 scopus 로고
    • Ground state magnetization of Ising spin glasses
    • F. Barahona, Ground state magnetization of Ising spin glasses. Phys. Rev. B 49 (1994) 2864-2867.
    • (1994) Phys. Rev. B , vol.49 , pp. 2864-2867
    • Barahona, F.1
  • 6
    • 0013152010 scopus 로고    scopus 로고
    • The volume algorithm: Producing primal solutions with a sub-gradient method
    • F. Barahona and R. Anbil, The volume algorithm: producing primal solutions with a sub-gradient method. Math. Program. 87 (2000) 385-399.
    • (2000) Math. Program. , vol.87 , pp. 385-399
    • Barahona, F.1    Anbil, R.2
  • 7
    • 84867967157 scopus 로고    scopus 로고
    • On some difficult linear programs coming from set partitioning
    • Third ALIO-EURO Meeting on Applied Combinatorial Optimization (Erice, 1990)
    • F. Barahona and R. Anbil, On some difficult linear programs coming from set partitioning. Discrete Appl. Math. 118 (2002) 3-11. Third ALIO-EURO Meeting on Applied Combinatorial Optimization (Erice, 1990).
    • (2002) Discrete Appl. Math. , vol.118 , pp. 3-11
    • Barahona, F.1    Anbil, R.2
  • 8
    • 0024012514 scopus 로고
    • An application of combinatorial optimization to statistical physics and circuit layout design
    • F. Barahona, M. Grötschel, M. Jünger and G. Reinelt. An application of combinatorial optimization to statistical physics and circuit layout design, Oper. Res. 36 (1988) 493-513.
    • (1988) Oper. Res. , vol.36 , pp. 493-513
    • Barahona, F.1    Grötschel, M.2    Jünger, M.3    Reinelt, G.4
  • 9
    • 0024681911 scopus 로고
    • Experiments in quadratic 0-1 programming
    • F. Barahona, M. Jünger and G. Reinelt, Experiments in quadratic 0-1 programming. Math. Program. 44 (1989) 127-137.
    • (1989) Math. Program. , vol.44 , pp. 127-137
    • Barahona, F.1    Jünger, M.2    Reinelt, G.3
  • 11
    • 33746201330 scopus 로고    scopus 로고
    • Annotated Bibliographies in Combinatorial Optimization, edited by M.D. Amico, F. Maffioli and S. Martello, Wiley
    • A. Caprara and M. Fischetti, Branch-and-cut algorithms, in Annotated Bibliographies in Combinatorial Optimization, edited by M.D. Amico, F. Maffioli and S. Martello, Wiley (1997) 45-63.
    • (1997) Branch-and-cut Algorithms , pp. 45-63
    • Caprara, A.1    Fischetti, M.2
  • 12
    • 0026880297 scopus 로고
    • Solving the Steiner tree problem in graphs using branch-and-cut
    • S. Chopra, E.R. Gorres and M.R. Rao, Solving the Steiner tree problem in graphs using branch-and-cut. ORSA J. Comput. 4 (1992) 320-335.
    • (1992) ORSA J. Comput. , vol.4 , pp. 320-335
    • Chopra, S.1    Gorres, E.R.2    Rao, M.R.3
  • 13
    • 33746193817 scopus 로고    scopus 로고
    • COIN-OR, http:www.coin-or.org.
  • 14
    • 21844508462 scopus 로고
    • Exact ground states of Ising spin glasses: New experimental results with a branch and cut algorithm
    • C. De Simone, M. Diehl, M. Jünger, P. Mutzel, G. Reinelt and G. Rinaldi, Exact ground states of Ising spin glasses: New experimental results with a branch and cut algorithm. J. Stat. Phys. 80 (1995) 487-496.
    • (1995) J. Stat. Phys. , vol.80 , pp. 487-496
    • De Simone, C.1    Diehl, M.2    Jünger, M.3    Mutzel, P.4    Reinelt, G.5    Rinaldi, G.6
  • 16
    • 0028728059 scopus 로고
    • A cutting plane algorithm for the max-cut problem. Optim
    • C. De Simone and G. Rinaldi, A cutting plane algorithm for the max-cut problem. Optim. Method. Softw. 3 (1994) 195-214.
    • (1994) Method. Softw. , vol.3 , pp. 195-214
    • De Simone, C.1    Rinaldi, G.2
  • 18
    • 21844516629 scopus 로고
    • A Lagrangean relax-and-cut approach for the sequential ordering problem with precedence relations
    • L.F. Escudero, M. Guignard and K. Malik, A Lagrangean relax-and-cut approach for the sequential ordering problem with precedence relations. Ann. Oper. Res. 50 (1994) 219-237.
    • (1994) Ann. Oper. Res. , vol.50 , pp. 219-237
    • Escudero, L.F.1    Guignard, M.2    Malik, K.3
  • 20
    • 27244458564 scopus 로고    scopus 로고
    • Optimizing over semimetric polytopes
    • Integer programming and combinatorial optimization, Springer, Berlin
    • A. Frangioni, A. Lodi and G. Rinaldi, Optimizing over semimetric polytopes, in Integer programming and combinatorial optimization, Springer, Berlin Lect. Notes Comput. Sci. 3064 (2004) 431-443.
    • (2004) Lect. Notes Comput. Sci. , vol.3064 , pp. 431-443
    • Frangioni, A.1    Lodi, A.2    Rinaldi, G.3
  • 21
    • 21144461865 scopus 로고
    • A catalog of Steiner tree formulations
    • M.X. Goemans and Y.S. Myung, A catalog of Steiner tree formulations, Networks 23 (1993), pp. 19-28.
    • (1993) Networks , vol.23 , pp. 19-28
    • Goemans, M.X.1    Myung, Y.S.2
  • 22
    • 0032002578 scopus 로고    scopus 로고
    • Efficient cuts in lagrangean "Relax-and-Cut" schemes
    • M. Guignard, Efficient cuts in lagrangean "Relax-and-Cut" schemes. Eur. J. Oper. Res. 105 (1998) 216-223.
    • (1998) Eur. J. Oper. Res. , vol.105 , pp. 216-223
    • Guignard, M.1
  • 23
    • 0001050402 scopus 로고
    • The travelling salesman problem and minimum spanning trees
    • M. Held and R.M. Karp, The travelling salesman problem and minimum spanning trees. Oper. Res. 18 (1970) 1138-1162.
    • (1970) Oper. Res. , vol.18 , pp. 1138-1162
    • Held, M.1    Karp, R.M.2
  • 24
    • 34250461535 scopus 로고
    • The travelling salesman problem and minimum spanning trees: Part II
    • M. Held and R.M. Karp, The travelling salesman problem and minimum spanning trees: Part II. Math. Program. 1 (1971) 6-25.
    • (1971) Math. Program. , vol.1 , pp. 6-25
    • Held, M.1    Karp, R.M.2
  • 25
    • 0016025814 scopus 로고
    • Validation of subgradient optimization
    • M. Held, P. Wolfe and H.P. Crowder, Validation of subgradient optimization. Math. Program. 6 (1974) 62-88.
    • (1974) Math. Program. , vol.6 , pp. 62-88
    • Held, M.1    Wolfe, P.2    Crowder, H.P.3
  • 26
    • 0041353723 scopus 로고    scopus 로고
    • Solving quadratic (0,1)-problems by semidefinite programs and cutting planes
    • C. Helmberg and F. Rendl, Solving quadratic (0,1)-problems by semidefinite programs and cutting planes. Math. Program. 82 (1998) 291-315.
    • (1998) Math. Program. , vol.82 , pp. 291-315
    • Helmberg, C.1    Rendl, F.2
  • 28
    • 0039986425 scopus 로고    scopus 로고
    • Solving Steiner tree problems in graphs to optimality
    • T. Koch and A. Martin, Solving Steiner tree problems in graphs to optimality, Networks 32 (1998) 207-232.
    • (1998) Networks , vol.32 , pp. 207-232
    • Koch, T.1    Martin, A.2
  • 29
    • 77957820648 scopus 로고
    • Nondifferentiable optimization
    • edited by G.L. Nemhauser, A.H.G. Rinnooy Kan and M.J. Todd, North Holland
    • C. Lemaréchal, Nondifferentiable optimization, in Optimization, Hanbooks Oper. Res., edited by G.L. Nemhauser, A.H.G. Rinnooy Kan and M.J. Todd, North Holland, 1989, pp. 529-572.
    • (1989) Optimization, Hanbooks Oper. Res. , pp. 529-572
    • Lemaréchal, C.1
  • 31
    • 2442635981 scopus 로고
    • Tight bounds for the Steiner problem in graphs
    • A. Lucena, Tight bounds for the Steiner problem in graphs, in Proc. Netflow 93 (1993) 147-154.
    • (1993) Proc. Netflow , vol.93 , pp. 147-154
    • Lucena, A.1
  • 32
    • 0040585116 scopus 로고    scopus 로고
    • A branch-and-cut algorithm for the Steiner problem in graphs
    • A. Lucena. and J. Beasley, A branch-and-cut algorithm for the Steiner problem in graphs. Networks 31 (1998), pp. 39-59.
    • (1998) Networks , vol.31 , pp. 39-59
    • Lucena, A.1    Beasley, J.2
  • 33
    • 0034345446 scopus 로고    scopus 로고
    • Computational experience with an interior point cutting plane algorithm
    • J.E. Mitchell, Computational experience with an interior point cutting plane algorithm. SIAM J. Optim. 10 (2000) 1212-1227.
    • (2000) SIAM J. Optim. , vol.10 , pp. 1212-1227
    • Mitchell, J.E.1
  • 34
    • 0026124209 scopus 로고
    • A branch-and-cut algorithm for the resolution of large-scale symmetric traveling salesman problems
    • M. Padberg and G. Rinaldi, A branch-and-cut algorithm for the resolution of large-scale symmetric traveling salesman problems. SIAM Rev. 33 (1991) 60-100.
    • (1991) SIAM Rev. , vol.33 , pp. 60-100
    • Padberg, M.1    Rinaldi, G.2
  • 35
    • 0035885223 scopus 로고    scopus 로고
    • Improved algorithms for the Steiner problem in networks
    • Combinatorial Optimization Symposium (Brussels, 1998)
    • T. Polzin and S.V. Daneshmand, Improved algorithms for the Steiner problem in networks. Discrete Appl. Math. 112 (2001) 263-300. Combinatorial Optimization Symposium (Brussels, 1998).
    • (2001) Discrete Appl. Math. , vol.112 , pp. 263-300
    • Polzin, T.1    Daneshmand, S.V.2
  • 36
    • 0000133156 scopus 로고
    • An approximated solution for the Steiner tree problem in graphs
    • H. Takahashi and A. Matsuyama, An approximated solution for the Steiner tree problem in graphs, Math. Japonica 254 (1980) 573-577.
    • (1980) Math. Japonica , vol.254 , pp. 573-577
    • Takahashi, H.1    Matsuyama, A.2
  • 37
    • 0141541601 scopus 로고    scopus 로고
    • Preprocessing Steiner problems from VLSI layout
    • E. Uchoa, M. Poggi de Aragão and C.C. Ribeiro, Preprocessing Steiner problems from VLSI layout, Networks 40 (2002) 38-50.
    • (2002) Networks , vol.40 , pp. 38-50
    • Uchoa, E.1    Poggi De Aragão, M.2    Ribeiro, C.C.3
  • 38
    • 0016621235 scopus 로고
    • A method of conjugate subgradients for minimizing nondifferentiable functions
    • P. Wolfe, A method of conjugate subgradients for minimizing nondifferentiable functions. Math. Program. Study 3 (1975) 145-173.
    • (1975) Math. Program. Study , vol.3 , pp. 145-173
    • Wolfe, P.1


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