Design of survivable networks: A survey

Networks

Volumn 46, Issue 1, 2005, Pages 1-21

  Kerivin, Hervé ^a   Mahjoub, A Ridha ^b  

^a UNIVERSITY OF MINNESOTA   (United States)

^b CNRS   (France)

Author keywords

Heuristic; Hop constraint; Polyhedral approach; Survivable network

Indexed keywords

GENERALIZED MULTIPROTOCOL LABEL SWITCHING (GMPLS); HOP-CONTRAINTS; POLYHEDRAL APPROACH; SURVIVAL NETWORKS;

ALGORITHMS; ASYNCHRONOUS TRANSFER MODE; HEURISTIC METHODS; NETWORK PROTOCOLS; OPTIMIZATION; ROBUSTNESS (CONTROL SYSTEMS); SET THEORY; TELECOMMUNICATION TRAFFIC; WAVELENGTH DIVISION MULTIPLEXING;

TELECOMMUNICATION NETWORKS;

EID: 23244465489     PISSN: 00283045     EISSN: None     Source Type: Journal    
DOI: 10.1002/net.20072     Document Type: Review

References (125)

1. A. Aggarwal and N. Garg, A scaling technique for better network design, Proc 5th Annual ACM-SIAM Symposium on Discrete Algorithms, 1994, pp. 233-240.
2. A. Aggarwal, P. Klein, and R. Ravi, When trees collapse: An approximation algorithm for the generalized Steiner problem in networks, SIAM J Comput 24 (1995), 440-456.
3. R.K. Ahuja, T.L. Magnanti, and J.B. Orlin, Network flows: Theory, algorithms, and applications, Prentice-Hall, Englewood Cliffs, NJ, 1993.
4. D. Alevras, M. Grötschel, and R. Wassäly, Capacity and survivability models for telecommunication networks, Technical Report SC 97-24, ZIP, Berlin, Germany, 1997.
5. M. Baïou, Le problème du sous-graphe Steiner 2-arête connexe: Approche polyédrale, Ph.D. Dissertation, Université de Rennes 1, Rennes, France, 1996.
6. M. Baïou, On the dominant of the Steiner 2-edge connected subgraph polytope, Discr Appl Math 112 (2001), 3-10.
7. M. Baïou, F. Barahona, and A.R. Mahjoub, Separation of partition inequalities, Math Oper Res 25 (2000), 243-254.
8. M. Baïou and A.R. Mahjoub, Steiner 2-edge connected subgraph polytopes on series-parallel graphs, SIAM J Discr Math 10 (1997), 505-514.
9. A. Balakrishnan and K. Altinkemer, Using a hop-constrained model to generate alternative communication network design, ORSA J Comput 4 (1992), 192-205.
10. A. Balakrishnan, T.L. Magnanti, and P. Mirchandani, Connectivity- splitting models for survivable network design, Networks 43 (2004), 10-27.
11. M.O. Ball, W.G. Liu, and W.R. Pulleyblank, Two terminal Steiner tree polyhedra, Technical Report CORR 87-33, University of Waterloo, Dept. of Combinatorics and Optimization, Waterloo, CA, 1987.
12. F. Barahona, Separating from the dominant of the spanning tree polytope, Oper Res Lett 12 (1992), 201-203.
13. F. Barahona and H. Kerivin, Separation of partition inequalities with terminals, Discr Optim 1 (2004), 129-140.
14. F. Barahona and A.R. Mahjoub, On two-connected subgraph polytopes, Discr Math 147 (1995), 19-34.
15. W. Ben-Ameur, Constrained length connectivity and survivable networks, Networks 36 (2000), 17-33.
16. W. Ben-Ameur and T.-T.-L. Pham, Design of survivable network based on end-to-end rerouting, Proc third international workshop of Design of Reliable Communication Networks, Budapest, Hungary, 2001, pp. 258-265.
17. D. Bienstock, E.F. Brickell, and C.L. Monma, On the structure of minimum-weight k-connected spanning networks, SIAM J Discr Math 3 (1990), 320-329.
18. D. Bienstock and G. Muratore, Strong inequalities for capacitated survivable network design problems, Math Program 89 (2001), 127-147.
19. A. Bley, On the complexity of vertex-disjoint length-restricted path problems, Computat Complexity 12(3-4) (2003), 131-149.
20. S.C. Boyd and T. Hao, An integer polytope related to the design of survivable communication networks, SIAM J Discr Math 6 (1993), 612-630.
21. S. Chopra, Polyhedra of the equivalent subgraph problem and some edge connectivity problems, SIAM J Discr Math 5 (1992), 321-337.
22. S. Chopra, The k-edge connected spanning subgraph polyhedron, SIAM J Discr Math 7 (1994), 245-259.
23. S. Chopra and M.R. Rao, The Steiner tree problem I: Formulations, compositions and extension of facets, Math Program 64 (1994), 209-229.
24. S. Chopra and M.R. Rao, The Steiner tree problem II: Properties and classes of facets, Math Program 64 (1994), 231-246.
25. S. Chopra and M. Stoer, Private communication.
26. W. Chou and H. Frank, Survivable communication networks and the terminal capacity matrix, IEEE Trans Circuit Theory 17 (1970), 183-192.
27. W. Chou and H. Frank, Connectivity communication networks and the terminal capacity matrix, IEEE Trans Circuit Theory 17 (1970), 486-490.
28. N. Christofides and C.A. Whitlock, "Network synthesis with connectivity constraints - A survey," Operational Research'81, J.P. Brans (Editor), North Holland, Amsterdam, 1981, pp. 705-723.
29. L.W. Clark and G. Anandalingam, A bootstrap heuristic for designing minimum cost survivable networks, Comput Oper Res 22 (1995), 921-924.
30. G. Cornuéjols, J. Fonlupt, and D. Naddef, The traveling salesman problem on a graph and some related integer polyhedra, Math Program 33 (1985), 1-27.
31. C.R. Coullard, A.B. Gamble, and J. Liu, "The K-walk polyhedron," Advances in optimization and approximation, D.-Z. Du and J. Sun (Editors), Kluwer Scientific Publishers, Norwell, 1994, pp. 9-29.
32. C.R. Coullard, A. Rais, R.L. Rardin, and D.K. Wagner, Linear-time algorithm for the 2-connected Steiner subgraph problem on special classes of graphs, Networks 23 (1993), 195-206.
33. 4-free graphs, Discr Appl Math 66 (1996), 195-206.
34. W.H. Cunningham, Optimal attack and reinforcement of a network, J ACM 32 (1985), 549-561.
35. G. Dahl, Contribution to the design of survivable directed networks, Ph.D. Dissertation, University of Oslo, Technical Report TF R 48/91, Norwegian Telecom, Research Dept, 1991.
36. G. Dahl, Directed Steiner problems with connectivity constraints, Discr Appl Math 47 (1993), 109-128.
37. G. Dahl, The 2-hop spanning tree problem, Oper Res Lett 23 (1998), 21-26.
38. G. Dahl, Notes on polyhedra associated with hop-constrained paths, Oper Res Lett 25 (1999), 97-100.
39. G. Dahl, N. Foldnes, and L. Gouveia, A note on hop-constrained walk polytopes, Oper Res Lett 32 (2004), 345-349.
40. G. Dahl and L. Gouveia, On the directed hop-constrained shortest path problem, Oper Res Lett 32 (2004), 15-22.
41. G. Dahl and B. Johannessen, The 2-path network design problem, Networks 43 (2004), 190-199.
42. G. Dahl and M. Stoer, A cutting plane algorithm for multicommodity survivable network design problems, INFORMS J Comput 10 (1998), 1-11.
43. M. Didi Biha, Graphes k-arête connexes et polyèdres, Ph.D. Dissertation, Université de Rennes 1, Rennes, France, 1998.
44. M. Didi Biha, H. Kerivin, and A.R. Mahjoub, Steiner trees and polyhedra, Discr Appl Math 112 (2001), 101-120.
45. M. Didi Biha, H. Kerivin, and A.R. Mahjoub, On the polytope of the (1,2)-survivable network design problem, Preprint, 2004.
46. M. Didi Biha and A.R. Mahjoub, k-Edge connected polyhedra on series-parallel graphs, Oper Res Lett 19 (1996), 71-78.
47. M. Didi Biha and A.R. Mahjoub, Steiner k-edge connected subgraph polyhedra, J Comb Optim 4 (2000), 131-144.
48. K.P. Eswaran and R.E. Tarjan, Augmentation problems, SIAM J Comput 5 (1976), 653-665.
49. J. Fonlupt and A.R. Mahjoub, Critical extreme points of the 2-edge connected spanning subgraph polytope, Proc IPCO'99, LNCS 1610, 1999, pp. 166-183.
50. J. Fonlupt and A.R. Mahjoub, Critical extreme points of the 2-edge connected spanning subgraph polytope, Math Program, to appear
51. [also available as Technical Report RR-04-17, LIMOS, Université Blaise Pascal, Clermont-Ferrand, France].
52. B. Fortz, Design of survivable networks with bounded rings, Kluwer Academic Publishers, Dordrecht, The Netherlands, 2000.
53. B. Fortz and M. Labbé, Polyhedral results for two-connected networks with bounded rings, Math Program 93 (2002), 27-54.
54. B. Fortz, M. Labbé, and F. Mafnoli, Solving the two-connected network with bounded meshes problem, Oper Res 48 (2000), 866-877.
55. B. Fortz, A.R. Mahjoub, S.T. McCormick, and P. Pesneau, The 2-edge connected subgraph problem with bounded rings, Math Program, to appear
56. [also available as Technical Report RR-04-18, LIMOS, Université Blaise Pascal, Clermont-Ferrand, France].
57. A. Frank, Augmenting graphs to meet edge-connectivity requirements, SIAM J Discr Math 5 (1992), 25-53.
58. G.N. Frederickson and J. Jájá, On the relationship between the biconnectivity augmentation problem and traveling salesman problem, Theoret Comput Sci 19 (1982), 189-201.
59. H.N. Gabow, M.X. Goemans, and D.P. Williamson, An efficient approximation algorithm for the survivable network design problem, Math Program 82 (1998), 13-40.
60. M.R. Garey and D.S. Johnson, Computers and intractability: A guide to the theory of NP-completeness, W. H. Freeman and Company, New York, 1979.
61. M.X. Goemans, The Steiner tree polytope and related polyhedra, Math Program 63 (1994), 157-182.
62. M.X. Goemans and D.J. Bertsimas, Survivable networks, linear-programming relaxations and the parsimonious property, Math Program 60 (1993), 145-166.
63. M.X. Goemans, A.V. Goldberg, S. Plotkin, D.B. Shmoys, E. Tardos, and D.P. Williamson, Approximation algorithms for network design problems, Proc SODA, 1994, pp. 223-232.
64. M.X. Goemans and D.P. Williamson, A general approximation technique for constrained forest problems, SIAM J Comput 24 (1995), 296-317.
65. M.X. Goemans and D.P. Williamson, "The primal-dual method for approximation algorithms and its application to network design problems," Approximation algorithms for NP-hard problems, D.S. Hochbaum (Editor), PWS Publishing Company, Boston, MA, 1997, pp. 144-191.
66. A.V. Goldberg and R.E. Tarjan, A new approach to the maximum-flow problem, J ACM 35 (1988), 921-940.
67. R.E. Gomory and T.C. Hu, Multi-terminal network flows, J Soc Indust Appl Math 9 (1961), 551-570.
68. L. Gouveia, Multicommodity flow models for spanning trees with hop constraints, Eur J Oper Res 95 (1996), 178-190.
69. L. Gouveia, Using variable redefinition for computing lower bounds for minimum spanning and Steiner trees with hop constraints, INFORMS J Comput 10 (1998), 180-188.
70. L. Gouveia and E. Janssen, Designing reliable tree networks with two cable technologies, Eur J Oper Res 105 (1998), 552-568.
71. L. Gouveia and T.L. Magnanti, Network flow models for designing diameter constrained spanning and Steiner trees, Networks 41 (2003), 159-173.
72. L. Gouveia, T.L. Magnanti, and C. Requejo, A 2-path approach for odd-diameter-constrained minimum spanning and Steiner trees, Networks 44 (2004), 254-265.
73. L. Gouveia, P. Patrício, and A. de Sousa, MPLS network design with fault-tolerance and hop constraints, Preprint, 2004.
74. L. Gouveia, P. Patrício, A. de Sousa, and R. Valadas, MPLS over WDM network design with packet level QoS constraints based on ILP models, Proc IEEE INFOCOM 2003, Vol. 1, 2003, pp. 576-586.
75. L. Gouveia and C. Requejo, A new Lagrangian relaxation approach for the hop-constrained minimum spanning tree problem, Eur J Oper Res 132 (2001), 539-552.
76. M. Grötschel, L. Lovász, and A. Schrijver, The ellipsoid method and its consequences in combinatorial optimization, Combinatorica 1 (1981), 70-89.
77. M. Grötschel and C.L. Monma, Integer polyhedra associated with certain network design problem with connectivity constraints, SIAM J Discr Math 3 (1990), 502-523.
78. 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(3) (1992), 474-504.
79. M. Grötschel, C.L. Monma, and M. Stoer, Computational results with a cutting plane algorithm for designing communication networks with low-connectivity constraints, Oper Res 40 (1992), 309-330.
80. M. Grötschel, C.L. Monma, and M. Stoer, "Design of survivable networks," Handbook in Operations Research and Management Science 7, M.O. Ball, C.L. Monma, and G. Nemhauser (Editors), North-Holland, Amsterdam, 1995, pp. 617-671.
81. D. Gusfield, Very simple algorithms and programs for all pairs network flow analysis, Computer Science Division, University of California, Davis, 1987.
82. T.-S. Hsu and M.-Y. Kao, A unifying augmentation algorithm for two-edge connectivity and biconnectivity, J Comb Optim 2 (1998), 237-256.
83. D. Huygens, A.R. Mahjoub, and P. Pesneau, Two edge-disjoint hop-constrained paths and polyhedra, SIAM J Discr Math 8(2) (2004), 287-312.
84. A. Itai, Y. Perl, and Y. Shiloach, The complexity of finding maximum disjoint paths with length constraints, Networks 12 (1982), 277-286.
85. K. Jain, A factor 2 approximation algorithm for the generalized Steiner network problem, Combinatorica 21 (2001), 39-60.
86. H. Kerivin, Réseaux fiables et polyèdres, Ph.D. Dissertation, Université Blaise Pascal, Clermont-Ferrand, France, 2000.
87. H. Kerivin and A.R. Mahjoub, Separation of the partition inequalities for the (1,2)-survivable network design problem, Oper Res Lett 30 (2002), 265-268.
88. H. Kerivin and A.R. Mahjoub, On survivable network polyhedra, Discr Math 290 (2005), 183-210.
89. H. Kerivin, A.R. Mahjoub, and C. Nocq, "(1,2)-survivable networks: Facets and branch-and-cut," The Sharpest Cut, MPS-SIAM Series in Optimization, M. Grötschel (Editor), MPS/SIAM, Philadelphia, 2004, pp. 121-152.
90. H. Kerivin, D. Nace, and T.-T.-L. Pham, Design of capacitated survivable networks with a single facility, IEEE/ACM Trans Networking, 13(2) (2005), 248-261.
91. S. Khuller and B. Raghavachari, Improved approximation algorithms for uniform connectivity problems, J Algorithms 21 (1996), 434-450.
92. S. Khuller and U. Vishkin, Biconnectivity approximation and graph carvings, J ACM 41 (1994), 214-235.
93. C-W. Ko and C.L. Monma, Heuristic methods for designing highly survivable communication networks, Technical Report, Bellcore, 1989.
94. E. Lawler, Combinatorial optimization: Networks and matroids, Holt, Rinehart and Winston, New York, 1976.
95. W.G. Liu, Extended formulations and polyhedral projection, Ph.D. Thesis, Dept. of Combinatorics and Optimization, University of Waterloo, 1988.
96. T.L. Magnanti and S. Raghavan, Strong formulations for network design problems with connectivity requirements, Networks 45(2) (2005), 61-79.
97. T. Magnanti and Y. Wang, Polyhedral properties of the network restoration problem - With the convex hull of a special case, MIT ORC Working Paper OR 323-97, 1997.
98. A.R. Mahjoub, Two-edge connected spanning subgraphs and polyhedra, Math Program 64 (1994), 199-208.
99. A.R. Mahjoub and C. Nocq, On the linear relaxation of the 2-node connected subgraph polytope, Discr Appl Math 95 (1999), 389-416.
100. A.R. Mahjoub and P. Pesneau, On the Steiner 2-edge connected polytope, Preprint, 2002.
101. F. Margot, A. Prodon, and T.M. Liebling, Tree polytope on 2-trees, Math Program 63 (1994), 183-191.
102. S.T. McCormick, Private communication.
103. K. Menger, Zur allgemeinen kurventheorie, Fundam Math 10 (1927), 96-115.
104. C.L. Monma, B.S. Munson, and W.R. Pulleyblank, Minimum-weight two connected spanning networks, Math Program 46 (1990), 153-171.
105. C.L. Monma and D.F. Shallcross, Methods for designing communication networks with certain two-connected survivability constraints, Oper Res 37 (1989), 531-541.
106. N.St.J.A. Nash-Williams, Edge-disjoint spanning trees of finite graphs, J Lond Math Soci 36 (1961), 445-450.
107. V.H. Nguyen, A complete linear description for the k-path polyhedron, Preprint, 2003.
108. M. Padberg and R. Rao, Odd minimum cutsets and b-matching, Math Oper Res 7 (1982), 67-80.
109. H. Pirkul and S. Soni, New formulations and solution procedures for the hop constrained network design problem, Eur J Oper Res 148 (2003), 126-140.
110. R. Ravi and D.P. Williamson, An approximation algorithm for minimum-cost vertex connectivity problems, Proc 6th Annual ACM-SIAM Symposium on Discrete Algorithms, 1995, pp. 332-341.
111. G. Reinelt, TSPLIB - A traveling salesman problem library, ORSA J Comput 3 (1991), 376-384.
112. A. Schrijver, Combinatorial optimization: Polyhedra and efficiency, Springer-Verlag, Berlin, 2003.
113. K. Steiglitz, P. Weigner, and D.J. Kleitman, The design of minimum-cost survivable networks, IEEE Trans Circuit Theory 16 (1969), 455-460.
114. M. Stoer, Design of survivable networks, Lecture notes in mathematics 1531, Springer-Verlag, Berlin, 1992.
115. M. Stoer and G. Dahl, A polyhedral approach to multicommodity survivable network design, Num Math 68 (1994), 149-167.
116. J.W. Suurballe, Disjoint paths in a network, Networks 4 (1974), 125-145.
117. J.W. Suurballe and R.E. Tarjan, A quick method for finding shortest pairs of disjoint paths, Networks 14 (1984), 325-336.
118. K. Takamizawa, T. Nishizeki, and N. Saito, Linear-time computability of combinatorial problems on series-parallel graphs, J ACM 29 (1982), 623-641.
119. W.T. Tutte, On the problem of decomposing a graph into n connected factors, J Lond Math Soci 36 (1961), 221-230.
120. D.P. Williamson, M.X. Goemans, M. Mihail, and V.V. Vazirani, A primal-dual approximation algorithm for generalized Steiner network problems, Combinatorica 15 (1995), 435-454.
121. P. Winter, Generalized Steiner problem in outerplanar networks, BIT 25 (1985), 485-496.
122. P. Winter, Generalized Steiner problem in series-parallel networks, J Algorithms 7 (1986), 549-566.
123. P. Winter, Steiner problem in Halin networks, Discr Appl Math (1987), 281-294.
124. P. Winter, Steiner problem in networks: a survey, Networks 17 (1987), 129-167.
125. T.H. Wu, Fiber networks service survivability, Artech House, Norwood, MA, 1992.