Minimum-Weight Rooted Not-Necessarily-Spanning Arborescence Problem

Networks

Volumn 39, Issue 2, 2002, Pages 77-87

  Rao, V Venkata ^a   Sridharan, R ^b  

^a INDIAN INSTITUTE OF MANAGEMENT   (India)

^b MASSEY UNIVERSITY   (New Zealand)

Author keywords

Acyclic graph; Arborescence; Heuristic; Lagrangian relaxation; NP hard; Tree; Uncapacitated plant location; Zero one integer programming

Indexed keywords

CONSTRAINT THEORY; HEURISTIC METHODS; INTEGER PROGRAMMING; ITERATIVE METHODS; LAGRANGE MULTIPLIERS;

LAGRANGIAN RELAXATION;

PROBLEM SOLVING;

EID: 0141651914     PISSN: 00283045     EISSN: None     Source Type: Journal    
DOI: 10.1002/net.10015     Document Type: Article

References (13)

1. G. Cornuejols, M.L. Fisher, and G.L. Nemhauser, On the uncapacitated plant location problem, Ann Discr Math 1 (1977), 163-177.
2. J. Edmonds, "Optimum branchings," Mathematics of the decision sciences, Part 1, G.B. Dantzig and A.F. Veinott, Jr. (Editors), American mathematical society lectures in applied mathematics, American Mathematical Society, Providence, RI, 1968, Vol. 11, pp. 335-345.
3. M. Fischetti and D. Vigo, A branch-and-cut algorithm for the resource-constrained minimum-weight arborescence problem, Networks 29 (1997), 55-67.
4. M.R. Garey and D.S. Johnson, Computers and intractability: A guide to the theory of NP-completeness, W.H. Freeman, San Francisco, 1979.
5. M.L. Goemans, Arborescence polytopes for series-parallel graphs, Discr Appl Math 51 (1994), 277-289.
6. L. Gouveia and E. Janssen, Designing reliable tree networks with two cable technologies, Eur J Oper Res 105 (1998), 552-568.
7. M. Held, P. Wolfe, and H.D. Crowder, Validation of sub-gradient optimization, Math Program 6 (1974), 62-88.
8. T.L. Magnanti and L.A. Wosley, "Optimal trees," Network models, Vol 7, Handbooks in operations research and management science, M. Ball, T.L. Magnanti, C.L. Monma, and G.L. Nemhauser (Editors), North Holland, Amsterdam, 1995, Chapter 9, pp. 503-615.
9. J.D. Murchland, Historical note on optimum spanning arborescences, Letter to the editor, Networks 3 (1973), 287-288.
10. V. Venkata Rao, Optimal lot sizing in acyclic multi-stage production systems, Ph.D. Dissertation, Georgia Institute of Technology, University Microfilms Order No. 8124 295, 1981.
11. V. Venkata Rao and L.F. McGinnis, The minimum weight rooted arborescence problem: A branch and bound solution, Working paper No. 514, Indian Institute of Management, Ahmedabad, June 1984.
12. V. Venkata Rao and R. Sridharan, The minimum weight rooted arborescence problem: Weights on arcs case, Working paper no. 1030, Indian Institute of Management, Ahmedabad, May 1992.
13. R.T. Wong, A dual ascent approach for Steiner tree problems on a directed graph, Math Program 28 (1984), 271-287.