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Volumn 381, Issue 1-3, 2004, Pages 117-139

The k-edge connected subgraph problem I: Polytopes and critical extreme points

Author keywords

Critical extreme point; Cut; k Edge connected graph; Polytope

Indexed keywords

POLYNOMIALS; PROBLEM SOLVING; RELIABILITY; TREES (MATHEMATICS); VECTORS;

EID: 1342285560     PISSN: 00243795     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.laa.2003.11.007     Document Type: Article
Times cited : (11)

References (27)
  • 1
    • 0037910900 scopus 로고    scopus 로고
    • Steiner 2-edge connected subgraph polytopes on series-parallel graphs
    • Baïou M., Mahjoub A.R. Steiner 2-edge connected subgraph polytopes on series-parallel graphs. SIAM J. Discrete Math. 10:1997;505-514.
    • (1997) SIAM J. Discrete Math. , vol.10 , pp. 505-514
    • Baïou, M.1    Mahjoub, A.R.2
  • 2
    • 0011355768 scopus 로고
    • On two-connected subgraph polytopes
    • Barahona F., Mahjoub A.R. On two-connected subgraph polytopes. Discrete Math. 147:1995;19-34.
    • (1995) Discrete Math. , vol.147 , pp. 19-34
    • Barahona, F.1    Mahjoub, A.R.2
  • 3
    • 0037572843 scopus 로고
    • On the structure of minimum weight k-connected spanning networks
    • Bienstock D., Brickell E.F., Monma C.L. On the structure of minimum weight. k-connected spanning networks SIAM J. Discrete Math. 3:1990;320-329.
    • (1990) SIAM J. Discrete Math. , vol.3 , pp. 320-329
    • Bienstock, D.1    Brickell, E.F.2    Monma, C.L.3
  • 4
    • 1342275235 scopus 로고
    • An integer polytope related to the design of survivable communication networks
    • Boyd S.C., Hao T. An integer polytope related to the design of survivable communication networks. SIAM J. Discrete Math. 5:1992;321-337.
    • (1992) SIAM J. Discrete Math. , vol.5 , pp. 321-337
    • Boyd, S.C.1    Hao, T.2
  • 5
    • 0042883409 scopus 로고
    • The k-edge connected spanning subgraph polyhedron
    • Chopra S. The. k-edge connected spanning subgraph polyhedron SIAM J. Discrete Math. 7:1994;245-259.
    • (1994) SIAM J. Discrete Math. , vol.7 , pp. 245-259
    • Chopra, S.1
  • 6
    • 0022129352 scopus 로고
    • The traveling salesman problem on a graph and some related integer polyhedra
    • Cornuéjols G., Fonlupt J., Naddef D. The traveling salesman problem on a graph and some related integer polyhedra. Math. Programming. 33:1985;1-27.
    • (1985) Math. Programming , vol.33 , pp. 1-27
    • Cornuéjols, G.1    Fonlupt, J.2    Naddef, D.3
  • 7
    • 0041881287 scopus 로고
    • The 2-connected-Steiner subgraph polytope for series-parallel graphs
    • School of Industrial Engineering, Purdue University
    • R. Coullard, A. Rais, R.L. Rardin, D.K. Wagner, The 2-connected-Steiner subgraph polytope for series-parallel graphs, Technical Report, School of Industrial Engineering, Purdue University, 1991.
    • (1991) Technical Report
    • Coullard, R.1    Rais, A.2    Rardin, R.L.3    Wagner, D.K.4
  • 8
    • 21144468818 scopus 로고
    • Linear-time algorithm for the 2-connected Steiner subgraph problem on special classes of graphs
    • Coullard R., Rais A., Rardin R.L., Wagner D.K. Linear-time algorithm for the 2-connected Steiner subgraph problem on special classes of graphs. Networks. 23:1993;195-206.
    • (1993) Networks , vol.23 , pp. 195-206
    • Coullard, R.1    Rais, A.2    Rardin, R.L.3    Wagner, D.K.4
  • 10
    • 0030212901 scopus 로고    scopus 로고
    • k-edge connected polyhedra on series-parallel graphs
    • Didi Biha M., Mahjoub A.R. k-edge connected polyhedra on series-parallel graphs Oper. Res. Lett. 19:1996;71-78.
    • (1996) Oper. Res. Lett. , vol.19 , pp. 71-78
    • Didi Biha, M.1    Mahjoub, A.R.2
  • 11
    • 0043186225 scopus 로고    scopus 로고
    • Steiner k-edge connected subgraph polyhedra
    • Didi Biha M., Mahjoub A.R. Steiner. k-edge connected subgraph polyhedra J. Combin. Optim. 4:2000;131-144.
    • (2000) J. Combin. Optim. , vol.4 , pp. 131-144
    • Didi Biha, M.1    Mahjoub, A.R.2
  • 12
    • 0000891810 scopus 로고
    • Algorithm for solution of a problem of maximum flow in a network with power estimation
    • Dinits E. Algorithm for solution of a problem of maximum flow in a network with power estimation. Soviet Math. Dokl. 11:1970;1277-1280.
    • (1970) Soviet Math. Dokl. , vol.11 , pp. 1277-1280
    • Dinits, E.1
  • 13
    • 0015330635 scopus 로고
    • Send-and-split method for minimum-concave-cost network flows
    • Edmonds J., Karp R. Send-and-split method for minimum-concave-cost network flows. J. Assoc. Comput. Mach. 19:1972;248-264.
    • (1972) J. Assoc. Comput. Mach. , vol.19 , pp. 248-264
    • Edmonds, J.1    Karp, R.2
  • 14
    • 84948995245 scopus 로고    scopus 로고
    • Critical extreme points of the 2-edge connected spanning subgraph polytope
    • Proceedings IPCO'99
    • J. Fonlupt, A.R. Mahjoub, Critical extreme points of the 2-edge connected spanning subgraph polytope, Proceedings IPCO'99, LNCS 1610, (1999), pp. 166-183.
    • (1999) LNCS , vol.1610 , pp. 166-183
    • Fonlupt, J.1    Mahjoub, A.R.2
  • 15
    • 0026759902 scopus 로고
    • The traveling salesman problem in graphs with some excluded minors
    • Fonlupt J., Naddef D. The traveling salesman problem in graphs with some excluded minors. Math. Programming. 53:1992;147-172.
    • (1992) Math. Programming , vol.53 , pp. 147-172
    • Fonlupt, J.1    Naddef, D.2
  • 16
    • 51249185617 scopus 로고
    • The ellipsoid method and its consequences in combinatorial optimization
    • Grötschel M., Lovász L., Schrijver A. The ellipsoid method and its consequences in combinatorial optimization. Combinatorica. 1:1981;70-89.
    • (1981) Combinatorica , vol.1 , pp. 70-89
    • Grötschel, M.1    Lovász, L.2    Schrijver, A.3
  • 17
    • 0000007148 scopus 로고
    • Integer polyhedra arising from certain net work design problems with connectivity constraints
    • Grötschel M., Monma C.L. Integer polyhedra arising from certain net work design problems with connectivity constraints. SIAM J. Discrete Math. 3:1990;502-523.
    • (1990) SIAM J. Discrete Math. , vol.3 , pp. 502-523
    • Grötschel, M.1    Monma, C.L.2
  • 19
    • 0001621683 scopus 로고
    • Computational results with a cutting plane algorithm for designing communication networks with low-connectivity constraints
    • Grötschel M., Monma C.L., Stoer M. Computational results with a cutting plane algorithm for designing communication networks with low-connectivity constraints. Oper. Res. 40:1992;309-330.
    • (1992) Oper. Res. , vol.40 , pp. 309-330
    • Grötschel, M.1    Monma, C.L.2    Stoer, M.3
  • 20
    • 0000312579 scopus 로고
    • Facets for polyhedra arising in the design of communication networks with low-connectivity constraints
    • Grötschel M., Monma C.L., Stoer M. Facets for polyhedra arising in the design of communication networks with low-connectivity constraints. SIAM J. Optim. 2:1992;474-504.
    • (1992) SIAM J. Optim. , vol.2 , pp. 474-504
    • Grötschel, M.1    Monma, C.L.2    Stoer, M.3
  • 21
    • 0029407103 scopus 로고
    • Polyhedral and computational investigations for designing communication networks with high survivability requirements
    • Grotschel M., Monma C.L., Stoer M. Polyhedral and computational investigations for designing communication networks with high survivability requirements. Oper. Res. 43:1995;1012-1024.
    • (1995) Oper. Res. , vol.43 , pp. 1012-1024
    • Grotschel, M.1    Monma, C.L.2    Stoer, M.3
  • 23
    • 0010867107 scopus 로고
    • Heuristic methods for designing highly survivable communication networks
    • Bell Communication Research
    • C.W. Ko, C.L. Monma, Heuristic methods for designing highly survivable communication networks, Technical Report, Bell Communication Research, 1989.
    • (1989) Technical Report
    • Ko, C.W.1    Monma, C.L.2
  • 24
    • 34249771292 scopus 로고
    • Two-edge connected spanning subgraphs and polyhedra
    • Mahjoub A.R. Two-edge connected spanning subgraphs and polyhedra. Math. Programming. 64:1994;199-208.
    • (1994) Math. Programming , vol.64 , pp. 199-208
    • Mahjoub, A.R.1
  • 25
    • 0042877877 scopus 로고    scopus 로고
    • On perfectly 2-edge connected graphs
    • Mahjoub A.R. On perfectly 2-edge connected graphs. Discrete Math. 95:1997;153-172.
    • (1997) Discrete Math. , vol.95 , pp. 153-172
    • Mahjoub, A.R.1
  • 26
    • 0024701993 scopus 로고
    • Methods for designing communication networks with certain two-connected survivability constraints
    • Monma C.L., Shallcross D.F. Methods for designing communication networks with certain two-connected survivability constraints. Oper. Res. 37:1989;531-541.
    • (1989) Oper. Res. , vol.37 , pp. 531-541
    • Monma, C.L.1    Shallcross, D.F.2
  • 27
    • 0004260999 scopus 로고
    • Design of Survivable Networks
    • Springer-Verlag
    • Stoer M. Design of Survivable Networks. Lecture Notes in Mathematics. 1992;Springer-Verlag.
    • (1992) Lecture Notes in Mathematics
    • Stoer, M.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.