Network Flow Models for Designing Diameter-Constrained Minimum-Spanning and Steiner Trees

Networks

Volumn 41, Issue 3, 2003, Pages 159-173

  Gouveia, Luis ^a   Magnanti, Thomas L ^b  

^a UNIVERSITY OF LISBON   (Portugal)

^b MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

Diameter constraints; Hop indexed models; Multicommodity flow models; Spanning trees; Steiner trees

Indexed keywords

DIAMETER CONSTRAINTS; HOP-INDEXED MODELS; MULTICOMMODITY FLOW MODELS; SPANNING TREES; STEINER TREES;

COMPUTATIONAL METHODS; COMPUTER AIDED NETWORK ANALYSIS; CONSTRAINT THEORY; GRAPH THEORY; HEURISTIC METHODS; INTEGER PROGRAMMING; LINEAR PROGRAMMING; OPTIMIZATION; POLYNOMIALS; PROBLEM SOLVING; RELIABILITY;

TREES (MATHEMATICS);

EID: 2142795873     PISSN: 00283045     EISSN: None     Source Type: Journal    
DOI: 10.1002/net.10069     Document Type: Article

References (21)

1. A. Abdalla, N. Deo, and R. Fraceschini, Parallel heuristics for the diameter-constrained minimum spanning tree problem, Congress Num 136 (1999), 97-118.
2. N.R. Achuthan, L. Caccetta, P. Caccetta, and J.F. Geelen, "Algorithms for the minimum weight spanning tree with bounded diameter problem," Optimization: techniques and applications, (P.H. Phua, C. Wang, W. Yeong, T. Leoug, H. Loh, K. Tau and F. Chou, Editors), World Scientific, Singapore 1992, Vol. 1, pp. 297-304.
3. N.R. Achuthan, L. Caccetta, P. Caccetta, and J. F. Geelen, Computational methods for the diameter restricted minimum weight spanning tree problem, Austral J Combin 10 (1994), 51-71.
4. A. Balakrishnan, and K. Altinkemer, Using a hop-constrained model to generate alternative communication network design, ORSA J Comput 4 (1992), 192-205.
5. A. Balakrishnan, T. Magnanti, and P. Mirchandani, Modelling and heuristic worst-case performance analysis of the two-level network design problem, Mgmt Sci 40 (1994), 846-867.
6. A. Balakrishnan, T. Magnanti, and R. Wong, A dual ascent procedure for large-scale uncapacitated network design, Oper Res 37 (1989), 716-740.
7. P. Camerini, G. Galbiati, and F. Maffioli, Complexity of spanning tree problems: Part I Eur J Oper Res 5 (1980), 346-352.
8. M. Garey and D. Johnson, Computers and intractability: A guide to the theory of NP-completeness, Freeman, San Francisco, 1979.
9. M. Goemans and Y. Myung, A catalog of Steiner tree formulations, Networks 23 (1993), 19-28.
10. L. Gouveia, Using the Miller-Tucker-Zemlin constraints to formulate a minimal spanning tree problem with hop constraints, Comput Oper Res 22 (1995), 959-970.
11. L. Gouveia, Multicommodity flow models for spanning trees with hop constraints, Eur J Oper Res 95 (1996), 178-190.
12. 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.
13. L. Gouveia and T. Magnanti, Network flow models for designing diameter constrained spanning and Steiner trees, Working paper 5/2000, Centro de Investigação Operacional, 2000.
14. G.Y. Handler, Minimax location of a facility in an undirected tree graph, Trans SCi 7 (1973), 287-293.
15. F. Hwang, D. Richards, and P. Winter, The Steiner tree problem, North-Holland, Amsterdam, 1992.
16. T. Magnanti and S. Raghavan, Strong formulations for network design problems with connectivity requirements, Working paper OR 332-99, Operations Research Center, MIT, April 1999.
17. T. Magnanti and L. Wolsey, Optimal trees, Handb Oper Res Mgmt SCi 7 (1996), 503-615.
18. T. Magnanti and R Wong, Network design and transportation planning: Models and algorithms., Tranp Sci 18 (1984), 1-55.
19. R. Martin, A sharp polynomial size linear programming formulation of the minimum spanning tree problem, Working paper, University of Chicago, 1986.
20. R.T. Wong, A dual ascent approach for Steiner tree problems on a directed graph, Math Program 28 (1984), 271-287.
21. K. Woolston and S. Albin, The design of centralized networks with reliability and availability constraints, Comput Oper Res 15 (1988), 207-217.