A Branch and Price algorithm for the k-splittable maximum flow problem

Discrete Optimization

Volumn 5, Issue 3, 2008, Pages 629-646

  Truffot, Jérôme ^a   Duhamel, Christophe ^a  

^a UNIVERSITÉ BLAISE PASCAL   (France)

Author keywords

Branch and Price; Column generation; Flow width; Max flow

Indexed keywords

ALGORITHMS; COMPUTATIONAL COMPLEXITY; CONSTRAINT THEORY; MATHEMATICAL MODELS; POLYNOMIALS; PROBLEM SOLVING;

BRANCH AND PRICE; COLUMN GENERATION; FLOW WIDTH; MAX FLOW;

FLOW PATTERNS;

EID: 43849113476     PISSN: 15725286     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.disopt.2008.01.002     Document Type: Article

References (24)

1. Ahuja R.K., Magnanti T.L., and Orlin J.B. Network Flows - Theory, Algorithms, and Applications (1993), Prentice Hall
2. Filipe Alvelos, José Manuel Vasconcelos Valério de Carvalho, Comparing branch-and-price algorithms for the unsplittable multicommodity flow problem, in: Proceedings of the International Network Optimization Conference, 2003, pp. 7-12
3. Atamtürk A., and Rajan D. On splittable and unsplittable capacitated network design arc-set polyhedra. Mathematical Programming 92 (2002) 315-333
4. Baier G., Köhler E., and Skutella M. On the k-splittable flow problem. Proceedings of the 10th Annual European Symposium on Algorithms (2002), Springer-Verlag 101-113
5. Barnhart C., Hane C.A., and Vance P.H. Using branch-and-price-and-cut to solve origin-destination integer multicommodity flow problems. Operations Research 48 2 (2000) 318-326
6. Barnhart C., Johnson E.L., Nemhauser G.L., Savelsbergh M.W.P., and Vance P.H. Branch-and-price: Column generation for solving huge integer programs. Operations Research 46 (1998) 316-329
7. James E. Burns, Teunis J. Ott, Johan M. de Kock, Anthony E. Krzesinski, Path selection and bandwidth allocation in MPLS networks: A non-linear programming approach, in: ITCom Conference, 2001
8. Dakin R.J. A tree-search algorithm for mixed integer programming problems. The Computer Journal 8 3 (1965) 250-254
9. Dantzig G.B., and Wolfe P. Decomposition principle for linear programs. Operations Research 8 (1960) 101-111
10. Ford L.R., and Fulkerson D.R. A suggested computation for maximal multicommodity network flow. Management Science 5 (1958) 97-101
11. R. Fukasawa, M. Poggi de Aragao, O. Porto, E. Uchoa, Robust branch-and-cut-and-price for the capacitated vehicle routing problem, in: INOC Conference, 2003, pp. 231-236
12. Jon M. Kleinberg, Approximation algorithms for disjoint paths problems, Ph.D. Thesis, Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1996
13. Ronald Koch, Martin Skutella, Ines Spenke, Approximation and complexity of k-splittable flows, in: WAOA, 2005, pp. 244-257
14. Kolliopoulos S. Minimum-cost single-source 2-splittable flow. Information Processing Letters 94 (2005) 15-18
15. Land A., and Doig A. An automatic method of solving discrete programming problems. Econometrika 28 3 (1960) 497-520
16. Lübbecke M.E., and Desrosiers J. Selected topics in column generation. Operations Research 53 6 (2005) 1007-1023
17. Maren Martens, Martin Skutella, Flows on few paths: Algorithms and lower bounds, in: Proceedings of ESA 2004, 2004, pp. 520-531
18. Maren Martens, Martin Skutella, Length-bounded and dynamic k-splittable flows, in: Proceedings of the International Scientific Annual Conference Operations Research, 2005
19. Martins E. The optimal path problem. Investigaçȧo Operacional 19 (1999) 43-60
20. Vahab S. Mirrokni, Marina Thottan, Huseyin Uzunalioglu, Sanjoy Paul, A simple polynomial time framework to reduced path decomposition in multi-path routing, in: Proceedings of INFOCOM 2004, 2004
21. Ryan D.M., and Foster B.A. An integer programming approach to scheduling. In: Wren A. (Ed). Computer Scheduling of Public Transport: Urban Passenger Vehicle and Crew Scheduling (1981), North-Holland Publishing Company 269-280
22. Sherali H.D., and Cole Smith J. Improving discrete model representations via symmetry considerations. Management Science 47 10 (2001) 1396-1407
23. Vanderbeck F., and Wolsey L.A. An exact algorithm for ip column generation. Operations Research Letters 19 4 (1996) 151-159
24. Bénédicte Vatinlen, Optimisation du routage dans les réseaux de télécommunication avec prise en compte de la qualité de service, Ph.D. Thesis, University Paris VI, 2004