T.L. Magnanti, L.A. Wolsey, Optimal Trees, Handbooks in Operations Research and Management Science, M.O. Ball, T.L. Magnanti, C.L. Monma, G.L. Nemhauser (Editors), Elsevier Science, Amsterdam, Vol. 7, Chap. 9 (1995) 503--615. Home/Search Document Not in Database Summary Related Articles Check |
This paper is cited in the following contexts:
The Generalized Minimum Spanning Tree Problem.. - Feremans.. (2002) (Correct)
....which is used to solve instances containing up to 75 vertices. Pop, Kern and Still [18] provide a polynomial approximation algorithm for the GMSTP. Its worst case ratio is bounded by 2# if the cluster size is bounded by #. This algorithm is derived from the method described in Magnanti and Wolsey [15] for the Vertex Weighted Steiner Tree Problem. The remainder of this article is organized as follows. In Section 2, we model the GMSTP by means of a tight integer linear programming formulation, and we also develop several families of valid inequalities. A polyhedral analysis is conducted in ....
....k K we find a subset S k containing V k for which the constraint x(E(S) 1, V k V, k K is violated. This is done by solving a maximum flow problem on an auxiliary undirected graph with capacities depending on the current solution (x # , y # ) and on k (see Magnanti and Wolsey [15] for this construction for the MSTP) The max flow algorithm used in our implementation is taken from Goldberg and Tarjan [11] For k K the auxiliary graph G( V , E) is defined as follows. Let V = V # t and E = E # v : v # v, t : v . The capacity for every ....
T.L. Magnanti, L.A. Wolsey, Optimal Trees, Handbooks in Operations Research and Management Science, M.O. Ball, T.L. Magnanti, C.L. Monma, G.L. Nemhauser (Editors), Elsevier Science, Amsterdam, Vol. 7, Chap. 9 (1995) 503--615.
Generalized Network Design Problems - Feremans, Labbé, Laporte (2002) (Correct)
....P on graph G(S T ) that spans T , and possibly some vertices from S. In this framework, feasible NDP solutions correspond to a subset of edges satisfying some constraints. Natural spanning NDPs are the following. 1. The Minimum Spanning Tree Problem (MSTP) see e.g. Magnanti and Wolsey [45]) The MSTP is to determine a minimum cost tree on G that includes all the vertices of V . This problem is polynomially solvable. 2. The Traveling Salesman Problem (TSP) see e.g. Lawler, Lenstra, Rinnooy Kan and Shmoys [42] The TSP consists of finding a minimum cost cycle that passes through ....
....bound obtained before branching is reduced by 10 to 20 . Pop, Kern and Still [51] provide a polynomial approximation algorithm for the E GMSTP. Its worst case ratio is bounded by 2# if the cluster size is bounded by #. This algorithm is derived from the method described in Magnanti and Wolsey [45] for the Vertex Weighted Steiner Tree Problem (see Section 9) Ihler, Reich, Widmayer [31] show that the decision version of the L GMSTP is NP complete even if G is a tree. They also prove that no constant worst case ratio polynomial time algorithm for the L GMSTP exists unless P = NP , ....
T.L. Magnanti, L.A. Wolsey, Optimal Trees, Handbooks in Operations Research and Management Science, M.O. Ball, T.L. Magnanti, C.L. Monma, G.L. Nemhauser (Editors), Elsevier Science, Amsterdam, Vol. 7, Chap. 9 (1995) 503--615.
Appia: Automatic Storage Area Network Fabric Design - Ward, O'Sullivan.. (2002) (5 citations) (Correct)
....paths. Each link has an associated fixed cost, and multiple links between a given pair of nodes may be selected. This problem contains the Steiner tree problem, known to be NP complete, in which one must find the minimum cost set of links to connect a given subset of the nodes in a network. See [23] for a survey of work on the Steiner tree problem. The nonbifurcated network loading problem is NP hard even when all commodities share a single source [21] If we relax the constraint that flows cannot be split, the SAN design problem generalizes the multicommodity network design problem [20, ....
T. L. Magnanti and L. A. Wolsey, Optimal trees,Network Models (M. O. Ball, T. L. Magnanti, C. L. Monma, and Nemhauser G. L., eds.), Handbooks in Operations Research and Management Science, vol. 7, North Holland, 1995, pp. 503--615.
Appia: Automatic Storage Area Network Fabric Design - Ward, O'Sullivan.. (2002) (5 citations) (Correct)
....so, multicommodity network design problems are notoriously difficult to solve in practice. This is true because their integer programming formulations LP relaxations do not provide tight lower bounds. Even finding feasible solutions is often difficult. Surveys of work in this area are given in [18, 1, 24]. In the NP hard problems mentioned above, one must find a minimum cost set of links to route the flows, when the nodes in the network are known. The SAN fabric design problem generalizes these problems, in that the nodes in the network are not known apriori. One must choose a set of hubs and ....
R.K. Ahuja, T.L. Magnanti, J.B. Orlin, and M.R. Reddy, Applications of network optimization, Network Models (M. O. Ball, T. L. Magnanti, C. L. Monma, and Nemhauser G. L., eds.), Handbooks in Operations Research and Management Science, vol. 7, North Holland, 1995, pp. 1--83.
Online articles have much greater impact More about CiteSeer.IST Add search form to your site Submit documents Feedback
CiteSeer.IST - Copyright Penn State and NEC