Steiner tree problems with profits

INFOR

Volumn 44, Issue 2, 2006, Pages 99-115

  Costa, Alysson M ^a   Cordeau, Jean François ^a   Laporte, Gilbert ^a  

^a HEC MONTRÉAL   (Canada)

Author keywords

Budget; Network design; Prize collecting; Quota; Reduction tests; Steiner tree problem

Indexed keywords

BUDGET CONTROL; COSTS; INDUSTRIAL ECONOMICS; PROBLEM SOLVING; PRODUCT DESIGN; TRAVELING SALESMAN PROBLEM;

BUDGETS; NETWORK DESIGN; PRIZE COLLECTING; QUOTA; REDUCTION TESTS; STEINER TREE PROBLEM;

TREES (MATHEMATICS);

EID: 33746597551     PISSN: 03155986     EISSN: None     Source Type: Journal    
DOI: 10.1080/03155986.2006.11732743     Document Type: Review

References (59)

1. Arya, S., and Ramesh, H. (1998). A 2.5 factor approximation algorithm for the k-MST problem, Information Processing Letters 65: 117-118.
2. Awerbuch, B., Azar, Y., Blum, A., and Vempala, S. (1998). New approximation guarantees for minimum-weight k-trees and prize-collecting salesmen, SIAM Journal on Computing 28: 254-262.
3. Balakrishnan, A., and Patel, N. (1987). Problem reduction methods and a tree generation algorithm for the Steiner network problem, Networks 17: 65-85.
4. Beasley, J. E. (1984). An algorithm for the Steiner problem in graphs, Networks 14: 147-159.
5. Beasley, J. E., and Nascimento, E. M. (1996). The vehicle routing-allocation problem: a unifying framework, TOP 4: 65-86.
6. Bienstock, D., Goemans, M. X., Simchi-Levi, D., and Williamson, D. (1993). A note on the prize collecting traveling salesman problem, Mathematical Programming 59: 413-420.
7. Canuto, S. A., Resende, M. G. C., and Ribeiro, C. C. (2001). Local search with perturbations for the prize-collecting Steiner tree problem in graphs, Networks 38: 50-58.
8. Chao, I.-M., Golden, B. L., and Wasil, E. A. (1996). A fast and effective heuristic for the orienteering problem, European Journal of Operational Research 88: 475-489.
9. Chawla, S., Kitchin, D., Rajan, U., Ravi, R., and Sinha, A. (2003). Profit maximizing mechanisms for the extended multicasting game, Proceedings of the 4th ACM Conference on Eletronic Commerce: 190-191.
10. Christofides, N. (1976). Worst-case analysis of a new heuristic for the travelling salesman problem, Technical Report 388 - Graduate School of Industrial Administration, Carnegie Mellon University.
11. Cole, R., Hariharan, R., Lewenstein, M., and Porat, E. (2001). A faster implementation of the Goemans-Williamson clustering algorithm, SODA'01: Proceedings of the Twelfth Annual ACM-SIAM Symposium on Discrete Algorithms: 17-25.
12. Courant, R., and Robbins, H. (1941). What is mathematics?, Oxford University Press. New York.
13. Cunha, A. S., Lucena, A., Maculan, N., and Resende, M. G. C. (2003). A relax and cut algorithm for the prize collecting Steiner problem in graphs, Proceeding of Mathematical Programming in Rio, Búzios - Brazil: 72-78.
14. Dantzig, G. B., Fulkerson, D. R., and Johnson, S. M. (1954). Solution of a large-scale traveling salesman problem, Operations Research 2: 393-410.
15. Dell'Amico, M., Maffioli, F., and Sciomachen, A. (1998). A Lagrangian heuristic for the prize-collecting travelling salesman problem, Annals of Operations Research 81: 289-305.
16. Duin, C. W., and Volgenant, A. (1987). Some generalizations of the Steiner problem in graphs, Networks 17: 353-364.
17. Duin, C. W., and Volgenant, A. (1989). Reduction tests for the Steiner problem in graphs, Networks 19: 549-567.
18. Engevall, S., Göthe-Lundgren, M., and Värbrand, P. (1998). A stronger lower bound for the node weighted Steiner tree problem, Networks 31: 11-17.
19. Feigenbaum, J., Papadimitriou, C. H., and Shenker, S. (2001). Sharing the cost of multicast transmissions, Journal of Computer and System Sciences 63: 21-41.
20. Feillet, D., Dejax, P., and Gendreau, M. (2005). Traveling salesman problems with profits, Transportation Science, 39: 188-205.
21. Fischetti, M., Salazar-González, J. J., and Toth, P. (1998). Solving the orienteering problem through branch-and-cut, INFORMS Journal on Computing 10: 133-148.
22. Fischetti, M., and Toth, P. (1988). An additive approach for the optimal solution of the prize-collecting travelling salesman problem, in B. L. Golden and A. A. Assad (eds), Vehicle Routing: Methods and Studies, North-Holland, Amsterdam.
23. Friedman, E. J., and Parkes, D. C. (2003). Pricing WiFi at Starbucks: issues in online mechanism design, Proceedings of the 4th ACM Conference on Electronic Commerce: 240-241.
24. Garey, M. R., Graham, R. L., and Johnson, D. S. (1977). The complexity of computing Steiner minimal trees, SIAM Journal on Applied Mathematics 32: 835-859.
25. Gendreau, M., Laporte, G., and Semet, F. (1998a). A branch-and-cut algorithm for the undirected selective travelling salesman problem, Networks 32: 263-273.
26. Gendreau, M., Laporte, G., and Semet, F. (1998b). A tabu search heuristic for the undirected selective travelling salesman problem, European Journal of Operational Research 106: 539-545.
27. Gilbert, E. N., and Pollak, H. O. (1968). Steiner minimal trees, SIAM Journal on Applied Mathematics 16: 1-29.
28. Goemans, M. X. (1994). The Steiner tree polytope and related polyhedra, Mathematical Programming 63: 157-182.
29. Goemans, M. X., and Williamson, D. P. (1995). A general approximation technique for constrained forest problems, SIAM Journal on Computing 24: 296-317.
30. Golden, B. L., Levy, L., and Vohra, R. (1987). The orienteering problem, Naval Research Logistics 34: 307-318.
31. Golden, B. L., Wang, Q., and Liu, L. (1988). A multifaceted heuristic for the orienteering problem,Naval Research Logistics 35: 359-366.
32. Guha, S., and Khuller, S. (1999). Improved methods for approximating node weighted Steiner trees and connected dominating sets, Information and Computation 150: 57-74.
33. Haouari, M., and Siala, J. C. (2006). A hybrid Lagrangian genetic algorithm for the prize collecting Steiner tree problem, Computers & Operations Research, 33: 1274-1288.
34. Hwang, F. K., Richards, D. S., and Winter, P. (1992). The Steiner Tree Problem, North-Holland, Amsterdan.
35. Johnson, D. S., Minkoff, M., and Phillips, S. (2000). The prize collecting Steiner tree problem: theory and practice, Proceedings of the 11th ACM-SIAM Symposium on Discrete Algorithms, San Francisco 760-769.
36. Kataoka, S., and Morito, S. (1988). An algorithm for the single constraint maximum collection problem, Journal of the Operations Research Society of Japan 31: 515-530.
37. Keller, C. P. (1989). Algorithms to solve the orienteering problem: a comparison, European Journal of Operational Research 41: 224-231.
38. Klau, G. W., Ljubić, I., Moser, A., Mutzel, P., Neuner, P., Pferschy, U., Raidl, G., and Weiskircher, R. (2004). Combining a memetic algorithm with integer programming to solve the prize-collecting Steiner tree problem, Springer Lecture Notes in Computer Science 3102: 1304-1315.
39. Klau, G. W., Ljubić, I., Mutzel, P., Pferschy, U., and Weiskircher, R. (2003). The fractional prize-collecting Steiner tree problem on trees, Technical Report TR-186-1-03-01, Institute of Computer Graphics and Algorithms, Vienna University of Technology.
40. Klein, P., and Ravi, R. (1995). A nearly best-possible approximation algorithm for node-weighted Steiner trees, Journal of Algorithms 19: 104-115.
41. Laporte, G., and Martello, S. (1990). The selective travelling salesman problem, Discrete Applied Mathematics 26: 193-207.
42. Laporte, G., and Rodríguez-Martín, I. (2006). Locating cycles in transportation and telecommunications networks, Networks. Forthcoming.
43. Lee, Y., Lim, B. H., and Park, J. S. (1996). A hub location problem in designing digital data service networks: Lagrangian relaxation approach, Location Science 4: 185-194.
44. Leifer, A. C., and Rosenwein, M. (1994). Strong linear programming relaxations for the orienteering problem, European Journal of Operational Research 73: 517-523.
45. Ljubić, I., Weiskircher, R., Pferschy, U., Klau, G., Mutzel, P., and Fischetti, M. (2004). Solving the prize-collecting Steiner tree problem to optimality, Technical Report TR 186-1-04-01, Institute of Computer Graphics and Algorithms, Vienna University of Technology.
46. Lucena, A. (1991). Tight bounds for the Steiner problem in graphs, Presentation made at the TIMS XXX - SOBRAPO XXIII Joint International Meeting, Rio de Janeiro, Brazil.
47. Lucena, A., and Resende, M. (2004). Strong lower bounds for the prize collecting Steiner problem in graphs, Discrete Applied Mathematics 141: 277-294.
48. Margot, F., Prodon, A., and Liebling, T. M. (1994). Tree polyhedron on 2-tree, Mathematical Programming 63: 183-192.
49. Megiddo, N. (1979). Combinatorial optimization with rational objective functions, Mathematics of Operations Research 4: 414-424.
50. Mittenthal, J., and Noon, C. E. (1992). Insert/delete heuristic for the travelling salesman subsettour problem with one additional constraint, Journal of the Operational Research Society 43: 277-283.
51. Mladenović, N., and Hansen, P. (1997). Variable neighborhood search, Computers & Operations Research 24: 1097-1100.
52. Prim, R. (1957). Shortest connection networks and some generalizations, Bell System Technology Journal 36: 1389-1401.
53. Ramesh, R., and Brown, K. M. (1991). An efficient four-phase heuristic for the generalized orienteering problem, Computers & Operations Research 18: 151-165.
54. Ramesh, R., Yoon, Y.-S., and Karwan, M. H. (1992). An optimal algorithm for the orienteering tour problem, ORSA Journal on Computing 4: 155-165.
55. Segev, A. (1987). The node-weighted Steiner tree problem, Networks 17: 1-17.
56. Tasgetiren, F. M., and Smith, A. E. (2000). A genetic algorithm for the orienteering problem, In Proceedings of the 2000 Congress on Evolutionary Computation, San Diego, USA: 1190-1195.
57. Tsiligirides, T. (1984). Heuristic methods applied to orienteering, Journal of the Operational Research Society 35: 797-809.
58. Uchoa, E. (2006). Reduction tests for the prize-collecting Steiner problem, Operations Research Letters, 34: 437-444.
59. Wang, Q., Sun, X., Golden, B. L., and Jia, J. (1995). Using artificial neural networks to solve the orienteering problem, Annals of Operations Research 61: 111-120.