Journal ArticleDOI
Minimal disconnecting sets in directed multi‐commodity networks
John J. Jarvis,John B. Tindall +1 more
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A finite algorithm similar to Gomory's, but requiring no more than m rows in the tableau, where m is the number of arcs in the network.Abstract:
The problem of finding minimal disconnecting sets for multi-commodity directed networks may be solved using an arc-path formulation and Gomory's all-integer integer programming algorithm. However, the number of network constraints may be astronomical for even moderately sized networks. This paper develops a finite algorithm similar to Gomory's, but requiring no more than m rows in the tableau, where m is the number of arcs in the network.read more
Citations
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Journal ArticleDOI
Multicommodity network flows—A survey
TL;DR: This report discusses solution techniques for both linear and nonlinear flow problems, which includes decomposition, partitioning, compact inverse methods, and primal-dual algorithms.
Journal ArticleDOI
A Survey of Linear Cost Multicommodity Network Flows
TL;DR: This exposition presents a state-of-the-art survey of results and algorithms for linear multicommodity network flow problems.
Journal ArticleDOI
Decomposition algorithms for locating minimal cuts in a network
John J. Jarvis,Suleyman Tufekci +1 more
TL;DR: The main theorem provides several cases for the algorithms and it is shown that the efficiency of one of the proposed algorithms is of the same order as a no-decomposition algorithm.
Full and Partial Multicommodity Cuts
TL;DR: In this paper, the problem of finding multicommodity cuts in graphs was investigated, and a polynomial algorithm for the T-planar problem was given for any fixed k unless the terminals are in non-crossing order.
Journal ArticleDOI
Decomposition algorithms for minimal cut problems
TL;DR: Under certain circumstances, the proposed one-node decomposition can produce a minimal cut for G in 0(n2 ) machine operations and it is shown that, under certain conditions, one- node cuts produce no decomposition.
References
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Book
Flows in networks
D. R. Ford,D. R. Fulkerson +1 more
TL;DR: Ford and Fulkerson as mentioned in this paper set the foundation for the study of network flow problems and developed powerful computational tools for solving and analyzing network flow models, and also furthered the understanding of linear programming.
Journal ArticleDOI
Flows in Networks.
TL;DR: The techniques presented by Ford and Fulkerson spurred the development of powerful computational tools for solving and analyzing network flow models, and also furthered the understanding of linear programming.
Journal ArticleDOI
Removing Arcs from a Network
TL;DR: An algorithm for making a sensitivity analysis on a flow network, specifically, the problem of removing n arcs in a network such that the reduction in the maximum flow between an origin and destination node is maximized is proposed.
Journal ArticleDOI
Optimal Defense of Multi-Commodity Networks
TL;DR: The determination of an optimal strategy for reinforcing arcs and nodes in a multi-commodity network is discussed and an algorithm for determining an optimal reinforcing strategy under certain assumptions is presented, and computational results are discussed.