Integer programming formulations for the two 4-hop-constrained paths problem

Networks

Volumn 49, Issue 2, 2007, Pages 135-144

  Huygens, David ^a   Mahjoub, A Ridha ^b  

^a UNIVERSITÉ LIBRE DE BRUXELLES   (Belgium)

^b UNIVERSITÉ BLAISE PASCAL   (France)

Author keywords

Edge disjoint paths; Hop constraint; Integer programming formulation; Node disjoint paths; Survivable network

Indexed keywords

CONSTRAINT THEORY; GRAPH THEORY; PROBLEM SOLVING;

EDGE DISJOINT PATHS; EDGE VERSIONS; INTEGER PROGRAMMING FORMULATION; NODE DISJOINT PATHS;

INTEGER PROGRAMMING;

EID: 34250661083     PISSN: 00283045     EISSN: 10970037     Source Type: Journal    
DOI: 10.1002/net.20147     Document Type: Article

References (24)

1. J.A. Bondy and U.S.R. Murty, Graph theory with applications, University Press, Belfast, 1976.
2. 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, 1994, pp. 9-29.
3. G. Dahl, The 2-hop spanning tree problem, Oper Res Lett 23 (1998), 21-26.
4. G. Dahl, Notes on polyhedra associated with hop-constrained paths, Oper Res Lett 25 (1999), 97-100.
5. G. Dahl, N. Foldnes, and L. Gouveia, A note on hop-constrained walk polytopes, Oper Res Lett 32 (2004), 345-349.
6. G. Dahl and L. Gouveia, On the directed hop-constrained shortest path problem, Oper Res Lett 32 (2004), 15-22.
7. G. Dahl, D. Huygens, A.R. Mahjoub, and P. Pesneau, On the k-edge disjoint 2-hop-constrained paths polytope, Oper Res Lett 34 (2006), 577-582.
8. G. Dahl and B. Johannessen, The 2-path network problem, Networks 43 (2004), 190-199.
9. 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.
10. L. Gouveia, Multicommodity flow models for spanning trees with hop constraints, Eur J Oper Res 95 (1996), 178-190.
11. 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.
12. L. Gouveia and E. Janssen, Designing reliable tree networks with two cable technologies, Eur J Oper Res 105 (1998), 552-568.
13. L. Gouveia and T. Magnanti, Network flow models for designing diameter-constrained minimum-spanning and Steiner trees, Networks 41 (2003), 159-173.
14. 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.
15. L. Gouveia, P. Patrício, 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, G. Anandalingam and S. Raghavan (Editors), Vol. 33, Springer, Berlin, 2005, pp. 167-180.
16. 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.
17. M. Grötschel, L. Lovász, and A. Schrijver, The ellipsoid method and its consequences in combinatorial optimization, Combinatorica 1 (1981), 70-89.
18. J. Hao and J.B. Orlin, A faster algorithm for finding the minimum cut in a directed graph, J Algor 17 (1994), 424-446.
19. 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, to appear in Networks.
20. D. Huygens, A.R. Mahjoub, and P. Pesneau, Two edge-disjoint hop-constrained paths and polyhedra, SIAM J Disc Math 18 (2004), 287-312.
21. H. Kerivin and A.R. Mahjoub, Design of survivable networks: A survey, Networks 46 (2005), 1-21.
22. A.R. Mahjoub and S.T. McCormick, The complexity of max flow and min cut with bounded-length paths, Preprint 2004.
23. V.H. Nguyen, A complete linear description for the k-path polyhedron, Preprint 2003.
24. W.R. Pulleyblank, "Polyhedral combinatorics," Optimization, Handbooks Oper Research and Management Science 1, G.L. Nemhauser, A.H.G. Rinnooy Kan, and M.J. Todd (Editors), North-Holland, Amsterdam, 1989, pp. 371-446.