메뉴 건너뛰기




Volumn 18, Issue 2, 2004, Pages 287-312

Two edge-disjoint HOP-constrained paths and polyhedra

Author keywords

Edge disjoint paths; Facet; Hop constraints; Polyhedron; Survivable network

Indexed keywords

GRAPH THEORY; INTEGER PROGRAMMING; POLYNOMIAL APPROXIMATION; PROBLEM SOLVING; SET THEORY; THEOREM PROVING;

EID: 18744376600     PISSN: 08954801     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0895480102419445     Document Type: Article
Times cited : (36)

References (38)
  • 1
    • 0026839532 scopus 로고
    • Using a hop-constrained model to generate alternative communication network design
    • A. BALAKRISHNAN AND K. ALTINKEMER, Using a hop-constrained model to generate alternative communication network design, ORSA J. Comput., 4 (1992), pp. 192-205.
    • (1992) ORSA J. Comput. , vol.4 , pp. 192-205
    • Balakrishnan, A.1    Altinkemer, K.2
  • 2
    • 0037910900 scopus 로고    scopus 로고
    • Steiner 2-edge connected subgraph polytopes on series-parallel graphs
    • M. BAÏOU AND A. R. MAHJOUB, Steiner 2-edge connected subgraph polytopes on series-parallel graphs, SIAM J. Discrete Math., 10 (1997), pp. 505-514.
    • (1997) SIAM J. Discrete Math. , vol.10 , pp. 505-514
    • Baïou, M.1    Mahjoub, A.R.2
  • 3
    • 0011355768 scopus 로고
    • On two-connected subgraphs polytopes
    • F. BARAHONA AND A. R. MAHJOUB, On two-connected subgraphs polytopes, Discrete Math., 147 (1995), pp. 19-34.
    • (1995) Discrete Math. , vol.147 , pp. 19-34
    • Barahona, F.1    Mahjoub, A.R.2
  • 4
    • 0034239439 scopus 로고    scopus 로고
    • Constrained length connectivity and survivable networks
    • W. BEN-AMEUR, Constrained length connectivity and survivable networks, Networks, 36 (2000), pp. 17-33.
    • (2000) Networks , vol.36 , pp. 17-33
    • Ben-Ameur, W.1
  • 5
    • 1442311554 scopus 로고    scopus 로고
    • Internet routing and related topology issues
    • W. BEN-AMEUR AND E. GOURDIN, Internet routing and related topology issues, SIAM J. Discrete Math., 17 (2003), pp. 18-49.
    • (2003) SIAM J. Discrete Math. , vol.17 , pp. 18-49
    • Ben-Ameur, W.1    Gourdin, E.2
  • 6
    • 0043186225 scopus 로고    scopus 로고
    • Steiner k-edge connected subgraph polytope
    • M. D. BIHA AND A. R. MAHJOUB, Steiner k-edge connected subgraph polytope, J. Comb. Optim., 4 (2000), pp. 131-144.
    • (2000) J. Comb. Optim. , vol.4 , pp. 131-144
    • Biha, M.D.1    Mahjoub, A.R.2
  • 7
    • 18744396597 scopus 로고    scopus 로고
    • On the complexity of vertex-disjoint length-restricted path problems
    • to appear
    • A. BLEY, On the complexity of vertex-disjoint length-restricted path problems, Comput. Complexity, to appear.
    • Comput. Complexity
    • Bley, A.1
  • 9
    • 0041720054 scopus 로고
    • An integer polytope related to the design of survivable communication networks
    • S. C. BOYD AND T. HAO, An integer polytope related to the design of survivable communication networks, SIAM J. Discrete Math., 6 (1993), pp. 612-630.
    • (1993) SIAM J. Discrete Math. , vol.6 , pp. 612-630
    • Boyd, S.C.1    Hao, T.2
  • 11
    • 0032131211 scopus 로고    scopus 로고
    • The 2-hop spanning tree problem
    • G. DAHL, The 2-hop spanning tree problem, Oper. Res. Lett., 23 (1998), pp. 21-26.
    • (1998) Oper. Res. Lett. , vol.23 , pp. 21-26
    • Dahl, G.1
  • 12
    • 0032680970 scopus 로고    scopus 로고
    • Notes on polyhedra associated with hop-constrained paths
    • G. DAHL, Notes on polyhedra associated with hop-constrained paths, Oper. Res. Lett., 25 (1999), pp. 97-100.
    • (1999) Oper. Res. Lett. , vol.25 , pp. 97-100
    • Dahl, G.1
  • 14
    • 2542615366 scopus 로고    scopus 로고
    • The 2-path network problem
    • G. DAHL AND B. JOHANNESSEN, The 2-path network problem, Networks, 43 (2004), pp. 190-199.
    • (2004) Networks , vol.43 , pp. 190-199
    • Dahl, G.1    Johannessen, B.2
  • 15
    • 84948995245 scopus 로고    scopus 로고
    • Critical extreme points of the 2-edge connected spanning subgaph polytope
    • Integer Programming and Combinatorial Optimization, G. Cornuéjols, R. E. Burkard, and G. J. Woeginger, eds., Springer-Verlag, Berlin
    • J. FONLUPT AND A. R. MAHJOUB, Critical extreme points of the 2-edge connected spanning subgaph polytope, in Integer Programming and Combinatorial Optimization, Lecture Notes in Comput. Sci. 1610, G. Cornuéjols, R. E. Burkard, and G. J. Woeginger, eds., Springer-Verlag, Berlin, 1999, pp. 166-182.
    • (1999) Lecture Notes in Comput. Sci. , vol.1610 , pp. 166-182
    • Fonlupt, J.1    Mahjoub, A.R.2
  • 16
    • 0034313847 scopus 로고    scopus 로고
    • Solving the two-connected network with bounded meshes problem
    • B. FORTZ, M. LABB, AND F. MAFFIOLI, Solving the two-connected network with bounded meshes problem, Oper. Res., 48 (2000), pp. 866-877.
    • (2000) Oper. Res. , vol.48 , pp. 866-877
    • Fortz, B.1    Labb, M.2    Maffioli, F.3
  • 17
    • 18744397147 scopus 로고    scopus 로고
    • The 2-edge connected subgraph problem with bounded rings
    • IAG, Université Catholique de Louvain, Louvain-la-Neuve, Belgium
    • B. FORTZ, A. R. MAHJOUB, S. T. MCCORMICK, AND P. PESNEAU, The 2-Edge Connected Subgraph Problem with Bounded Rings, Working paper 98/03, IAG, Université Catholique de Louvain, Louvain-la-Neuve, Belgium, 2003.
    • (2003) Working Paper , vol.98 , Issue.3
    • Fortz, B.1    Mahjoub, A.R.2    Mccormick, S.T.3    Pesneau, P.4
  • 18
    • 0008774744 scopus 로고    scopus 로고
    • An efficient approximation algorithm for the survivable network design problem, Networks and matroids; Sequencing and scheduling
    • H. N. GABOW, M. X. GOEMANS, AND D. P. WILLIAMSON, An efficient approximation algorithm for the survivable network design problem, Networks and matroids; Sequencing and scheduling. Math. Programming, 82 (1998), pp. 13-40.
    • (1998) Math. Programming , vol.82 , pp. 13-40
    • Gabow, H.N.1    Goemans, M.X.2    Williamson, D.P.3
  • 19
    • 0030283804 scopus 로고    scopus 로고
    • Multicommodity flow models for spanning trees with hop constraints
    • L. GOUVEIA, Multicommodity flow models for spanning trees with hop constraints, European J. Oper. Res., 95 (1996), pp. 178-190.
    • (1996) European J. Oper. Res. , vol.95 , pp. 178-190
    • Gouveia, L.1
  • 20
    • 0001276437 scopus 로고    scopus 로고
    • Using variable redefinition for computing lower bounds for minimum spanning and Steiner trees with hop constraints
    • L. GOUVEIA, Using variable redefinition for computing lower bounds for minimum spanning and Steiner trees with hop constraints, INFORMS J. Comput., 10 (1998), pp. 180-188.
    • (1998) Informs J. Comput. , vol.10 , pp. 180-188
    • Gouveia, L.1
  • 21
    • 0032028626 scopus 로고    scopus 로고
    • Designing reliable tree networks with two cable technologies
    • L. GOUVEIA AND E. JANSSEN, Designing reliable tree networks with two cable technologies, European J. Oper. Res., 105 (1998), pp. 552-568.
    • (1998) European J. Oper. Res. , vol.105 , pp. 552-568
    • Gouveia, L.1    Janssen, E.2
  • 22
    • 18744381511 scopus 로고    scopus 로고
    • Modelling and solving the diameter-constrained minimum spanning tree problem
    • DEIO-CIO, Faculdade de Ciências da Universidade de Lisboa
    • L. GOUVEIA AND T. L. MAGNANTI, Modelling and Solving the Diameter-Constrained Minimum Spanning Tree Problem, Technical report, DEIO-CIO, Faculdade de Ciências da Universidade de Lisboa, 2000.
    • (2000) Technical Report
    • Gouveia, L.1    Magnanti, T.L.2
  • 23
    • 0035427762 scopus 로고    scopus 로고
    • A new Lagrangean relaxation approach for the hop-constrained minimum spanning tree problem
    • L. GOUVEIA AND C. REQUEJO, A new Lagrangean relaxation approach for the hop-constrained minimum spanning tree problem, European J. Oper. Res., 132 (2001), pp. 539-552.
    • (2001) European J. Oper. Res. , vol.132 , pp. 539-552
    • Gouveia, L.1    Requejo, C.2
  • 24
    • 51249185617 scopus 로고
    • The ellipsoid method and its consequences in combinatorial optimization
    • M. GRÖTSCHEL, L. LOVÁSZ, AND A. SCHRIJVER, The ellipsoid method and its consequences in combinatorial optimization, Combinatorica, 1 (1981), pp. 169-197.
    • (1981) Combinatorica , vol.1 , pp. 169-197
    • Grötschel, M.1    Lovász, L.2    Schrijver, A.3
  • 25
    • 0000007148 scopus 로고
    • Integer polyhedra arising from certain networks design problems with connectivity constraints
    • M. GRÖTSCHEL AND C. L. MONMA, Integer polyhedra arising from certain networks design problems with connectivity constraints, SIAM J. Discrete Math., 3 (1990), pp. 502-523.
    • (1990) SIAM J. Discrete Math. , vol.3 , pp. 502-523
    • Grötschel, M.1    Monma, C.L.2
  • 26
    • 0041881283 scopus 로고
    • Polyhedral approaches to network survivability
    • Reliability of Computer and Communication Networks, F. Roberts, F. Hwang, and C. L. Monma eds., AMS, Providence, RI
    • M. GRÖTSCHEL, C. L. MONMA, AND M. STOER, Polyhedral approaches to network survivability, in Reliability of Computer and Communication Networks, DIMACS Ser. Discrete Math. Theoret. Comput. Sci. 5, F. Roberts, F. Hwang, and C. L. Monma eds., AMS, Providence, RI, 1991, pp. 121-141.
    • (1991) DIMACS Ser. Discrete Math. Theoret. Comput. Sci. , vol.5 , pp. 121-141
    • Grötschel, M.1    Monma, C.L.2    Stoer, M.3
  • 27
    • 0000312579 scopus 로고
    • Facets for polyhedra arising in the design of communication networks with low-connectivity constraints
    • M. GRÖTSCHEL, C. L. MONMA, AND M. STOER, Facets for polyhedra arising in the design of communication networks with low-connectivity constraints, SIAM J. Optim., 2 (1992), pp. 474-504.
    • (1992) SIAM J. Optim. , vol.2 , pp. 474-504
    • Grötschel, M.1    Monma, C.L.2    Stoer, M.3
  • 28
    • 77957077046 scopus 로고
    • Design of survivable networks
    • Network Models, M. O. Ball, T. L. Magnanti, C. L. Monma, and G. L. Nemhauser, eds., North-Holland, Amsterdam
    • M. GRÖTSCHEL, C. L. MONMA, AND M. STOER, Design of survivable networks, in Network Models, Handbooks Oper. Res. Management Sci. 7, M. O. Ball, T. L. Magnanti, C. L. Monma, and G. L. Nemhauser, eds., North-Holland, Amsterdam, 1995, pp. 617-671.
    • (1995) Handbooks Oper. Res. Management Sci. , vol.7 , pp. 617-671
    • Grötschel, M.1    Monma, C.L.2    Stoer, M.3
  • 29
    • 0008824980 scopus 로고
    • A faster algorithm for finding the minimum cut in a directed graph
    • J. HAO AND J. B. ORLIN, A faster algorithm for finding the minimum cut in a directed graph, J. Algorithms, 17 (1994), pp. 424-446.
    • (1994) J. Algorithms , vol.17 , pp. 424-446
    • Hao, J.1    Orlin, J.B.2
  • 30
    • 0020175940 scopus 로고
    • The complexity of finding maximum disjoint paths with length constraints
    • A. ITAI, Y. PERL, AND Y. SHILOACH, The complexity of finding maximum disjoint paths with length constraints, Networks, 12 (1982), pp. 277-286.
    • (1982) Networks , vol.12 , pp. 277-286
    • Itai, A.1    Perl, Y.2    Shiloach, Y.3
  • 31
    • 0005363324 scopus 로고    scopus 로고
    • A factor 2 approximation algorithm for the generalized Steiner network problem
    • K. JAIN, A factor 2 approximation algorithm for the generalized Steiner network problem, Combinatorica, 21 (2001), pp. 39-60.
    • (2001) Combinatorica , vol.21 , pp. 39-60
    • Jain, K.1
  • 32
    • 1342317475 scopus 로고    scopus 로고
    • (1, 2)-survivable networks: Facets and branch-and-cut
    • The Sharpest Cut: The Impact of Manfred Padberg and His Work, M. Grötschel, ed., SIAM, Philadelphia
    • H. KERIVIN, A. R. MAHJOUB, AND C. NOCQ, (1, 2)-survivable networks: Facets and branch-and-cut, in The Sharpest Cut: The Impact of Manfred Padberg and His Work, MPS/SIAM Ser. Optim., M. Grötschel, ed., SIAM, Philadelphia, 2004, pp. 121-152.
    • (2004) MPS/SIAM Ser. Optim. , pp. 121-152
    • Kerivin, H.1    Mahjoub, A.R.2    Nocq, C.3
  • 33
    • 77955486913 scopus 로고
    • Reliable link topology/capacity and routing in backbone telecommunication networks
    • Owen Graduate School of Management, Vanderbilt University, Nashville, TN
    • L. J. LEBLANC AND R. REDDOCH, Reliable Link Topology/Capacity and Routing in Backbone Telecommunication Networks, Working paper 90-08, Owen Graduate School of Management, Vanderbilt University, Nashville, TN, 1990.
    • (1990) Working Paper , vol.90 , Issue.8
    • Leblanc, L.J.1    Reddoch, R.2
  • 34
    • 0012590682 scopus 로고    scopus 로고
    • Packet routing in telecommunications networks with path and flow restrictions
    • L. J. LEBLANC, R. REDDOCH, J. CHIFFLET, AND P. MAHEY, Packet routing in telecommunications networks with path and flow restrictions, INFORMS J. Comput., 11 (1999), pp. 188-197.
    • (1999) INFORMS J. Comput. , vol.11 , pp. 188-197
    • Leblanc, L.J.1    Reddoch, R.2    Chifflet, J.3    Mahey, P.4
  • 35
    • 85013990412 scopus 로고
    • Finding disjoint paths with different path-costs: Complexity and algorithms
    • C.-L. LI, S. T. MCCORMICK, AND D. SIMCHI-LEVI, Finding disjoint paths with different path-costs: Complexity and algorithms, Networks, 22 (1992), pp. 653-667.
    • (1992) Networks , vol.22 , pp. 653-667
    • Li, C.-L.1    McCormick, S.T.2    Simchi-Levi, D.3
  • 36
    • 34249771292 scopus 로고
    • Two-edge connected spanning subgraphs and polyhedra
    • A. R. MAHJOUB, Two-edge connected spanning subgraphs and polyhedra, Math. Programming, 64 (1994), pp. 199-208.
    • (1994) Math. Programming , vol.64 , pp. 199-208
    • Mahjoub, A.R.1
  • 37
    • 0037411037 scopus 로고    scopus 로고
    • New formulations and solution procedures for the hop constrained network design problem
    • H. PIRKUL AND S. SONI, New formulations and solution procedures for the hop constrained network design problem, European J. Oper. Res., 148 (2003), pp. 126-140.
    • (2003) European J. Oper. Res. , vol.148 , pp. 126-140
    • Pirkul, H.1    Soni, S.2
  • 38
    • 77957039738 scopus 로고
    • Polyhedral combinatorics
    • Optimization, G. L. Nemhauser, A. H. G. Rinnooy Kan, and M. J. Todd, eds., North-Holland, Amsterdam
    • W. R. PULLEYBLANK, Polyhedral combinatorics, in Optimization, Handbooks Oper. Res. Management Sci. 1, G. L. Nemhauser, A. H. G. Rinnooy Kan, and M. J. Todd, eds., North-Holland, Amsterdam, 1989, pp. 371-446.
    • (1989) Handbooks Oper. Res. Management Sci. , vol.1 , pp. 371-446
    • Pulleyblank, W.R.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.