A new approach to the maximum flow problem
STOC '86 Proceedings of the eighteenth annual ACM symposium on Theory of computing
Combinatorial optimization: algorithms and complexity
Combinatorial optimization: algorithms and complexity
Introduction to algorithms
Network flows: theory, algorithms, and applications
Network flows: theory, algorithms, and applications
Experimental study of minimum cut algorithms
SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
Enumerating disjunctions and conjunctions of paths and cuts in reliability theory
Discrete Applied Mathematics
Minimum-cost optimization in multicommodity logistic chain network
IWMM'04/GIAE'04 Proceedings of the 6th international conference on Computer Algebra and Geometric Algebra with Applications
| Hi-index | 0.01 |
Cutset algorithms have been well documented in the operations research literature. A directed graph is used to model the network, where each node and arc has an associated cost to cut or remove it from the graph. The problem considered in this paper is to determine all minimum cost sets of nodes and/or arcs to cut so that no directed paths exist from a specified source node s to a specified sink node t. By solving the dual maximum flow problem, it is possible to construct a binary relation associated with an optimal maximum flow such that all minimum cost s-t cutsets are identified through the set of closures for this relation. The key to our implementation is the use of graph theoretic techniques to rapidly enumerate this set of closures. Computational results are presented to suggest the efficiency of our approach.