The two-edge connected hop-constrained network design problem: Valid inequalities and branch-and-cut

Networks

Volumn 49, Issue 1, 2007, Pages 116-133

  Huygens, David ^a   Labbé, Martine ^a   Mahjoub, A Ridha ^b   Pesneau, Pierre ^c,d  

^a UNIVERSITÉ LIBRE DE BRUXELLES   (Belgium)

^b UNIVERSITÉ BLAISE PASCAL   (France)

^c UNIVERSITÉ CATHOLIQUE DE LOUVAIN   (Belgium)

^d UNIVERSITÉ BORDEAUX 1   (France)

Author keywords

Branch and cut; Edge connectivity; Facets; Hop constraints; Network design; NP hardness; Valid inequalities

Indexed keywords

ALGORITHMS; COMPUTATIONAL COMPLEXITY; GRAPH THEORY; INTEGER PROGRAMMING; POLYNOMIALS;

BRANCH-AND-CUT; EDGE CONNECTIVITY; FACETS; HOP-CONSTRAINTS; NETWORK DESIGN; VALID INEQUALITIES;

PROBLEM SOLVING;

EID: 33947579670     PISSN: 00283045     EISSN: 10970037     Source Type: Journal    
DOI: 10.1002/net.20146     Document Type: Conference Paper

References (34)

1. A. Balakrishnan and K. Altinkemer, Using a hop-constrained model to generate alternative communication network design, ORSA J Comput 4 (1992), 192-205.
2. W. Ben-Ameur, Constrained length connectivity and survivable networks, Networks 36 (2000), 17-33.
3. W. Ben-Ameur and E. Gourdin, Internet routing and related topology issues, SIAM J Discrete Math 17 (2003), 18-49.
4. J.A. Bondy and U.S.R. Murty, Graph theory with applications, Universities Press, Belfast, 1976.
5. 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 Academic Publishers, New York, 1994, pp. 9-29.
6. G. Dahl, The 2-hop spanning tree problem, Oper Res Lett 23 (1998), 21-26.
7. [7 ] G. Dahl, Notes on polyhedra associated with hop-constrained paths, Oper Res Lett 25 (1999), 97-100.
8. G. Dahl, N. Foldnes, and L. Gouveia, A note on hop-constrained walk polytopes, Oper Res Lett 32 (2004), 345-349.
9. G. Dahl and L. Gouveia, On the directed hop-constrained shortest path problem, Oper Res Lett 32 (2004), 15-22.
10. G. Dahl, D. Huygens, A.R. Mahjoub, and P. Pesneau, On the k-edge disjoint 2-hop-constrained paths polytope, 2005, Oper Res Lett 34 (2006), 577-582.
11. G. Dahl and B. Johannessen, The 2-path network problem, Networks 43 (2004), 190-199.
12. B. Fortz, A.R. Mahjoub, S.T. McCormick, and P. Pesneau, Two-edge connected subgraphs with bounded rings: Polyhedral results and branch-and-cut, Math Prog 105 (2006), 85-111.
13. M.R. Garey and D.S. Johnson, Computers and intractability: A guide to the theory of NP-completeness, Freeman, New York, 1979.
14. M.X. Goemans and V.S. Ramakrishnan, Minimizing sub-modular functions over families of sets, Combinatorica 15 (1995), 499-513.
15. R.E. Gomory and T.C. Hu, Multi-terminal network flows, SIAM J Appl Math 9 (1961), 551-570.
16. L. Gouveia, Multicommodity flow models for spanning trees with hop constraints, Eu J Oper Res 95 (1996), 178-190.
17. 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.
18. L. Gouveia and E. Janssen, Designing reliable tree networks with two cable technologies, Eur J Oper Res 105 (1998), 552-568.
19. L. Gouveia and T. Magnanti, Network flow models for designing diameter-constrained minimum-spanning and Steiner trees, Networks 41 (2003), 159-173.
20. L. Gouveia, T. Magnanti, and C. Requejo, A 2-path approach for odd-diameter-constrained minimum spanning and Steiner trees, Networks 44 (2004), 254-265.
21. L. Gouveia, P. Patricio, and A. de Sousa, "Compact models for hop-constrained node survivable network design, an application to MPLS," Telecommunications planning: Innovations in pricing, network design and management, S. Raghavan and G. Anandalingam (Editors), Vol. 33, Springer, Berlin, 2006, pp. 167-180.
22. L. Gouveia and C. Requejo, A new Lagrangean relaxation approach for the hop-constrained minimum spanning tree problem, Eur J Oper Res 132 (2001), 539-552.
23. D. Gusfield, Very simple methods for all pairs network flow analysis, SIAM J Comput 19 (1990), 143-155.
24. D. Huygens, M. Labbé, A. Mahjoub, and P. Pesneau, The 2-edge connected hop-constrained network design problem: Valid inequalities and branch-and-cut. Tech. Rep. RR-06:02, LIMOS, Université Blaise Pascal, Clermont-Ferrand, France, 2006.
25. D. Huygens and A.R. Mahjoub, Integer programming formulations for the two 4-hop-constrained paths problem, Preprint, 2005.
26. D. Huygens, A.R. Mahjoub, and P. Pesneau, Two edge-disjoint hop-constrained paths and polyhedra, SIAM J Discrete Math 18 (2004), 287-312.
27. ILOG, S.A., ILOG Cplex 8.11: User's Manual and Reference Manuals, 2003. http://www.ilog.com/.
28. H. Kerivin and A.R. Mahjoub, Design of survivable networks: A survey, Networks 46 (2005), 1-21.
29. 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.
30. 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), 188-197.
31. R. Lougee-Heimer, The common optimization interface for operations research, IBM J Res Dev 47 (2003), 57-66.
32. 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.
33. W.R. Pulleyblank, "Polyhedral combinatorics," Optimization, Handbooks Oper Res Management Sci 1, G.L. Nemhauser, A.H.G. Rinnooy Kan, and M.J. Todd (Editors), North-Holland, Amsterdam, 1989, pp. 371-446.
34. A. Schrijver, Combinatorial optimization: Polyhedra and efficiency, Volume B, Matroids, trees, stable sets, Chapters 39-69, Springer, Berlin, 2003.