On the structure of all minimum cuts in a network and applications

This paper presents a characterization of all minimum cuts, separating a source from a sink in a network. A binary relation is associated with any maximum flow in this network, and minimum cuts are identified with closures for this relation. As a consequence, finding all minimum cuts reduces to a straightforward enumeration. Applications of this results arise in sensitivity and parametric analyses of networks, the vertex packing and maximum closure problems, in unconstrained pseudo-boolean optimization and project selection, as well as in other areas of application of minimum cuts.

[1]  S. Lubore,et al.  Determining the most vital link in a flow network , 1971 .

[2]  J. Picard.  Maximal Closure of a Graph and Applications to Combinatorial Problems , 1976 .

[3]  Richard L. Francis,et al.  EVACNET: Prototype Network Optimization Models for Building Evacuation. | NIST , 1979 .

[4]  G. Grätzer,et al.  Lattice Theory: First Concepts and Distributive Lattices , 1971 .

[5]  Donald Watts Davies,et al.  Communication Networks for Computers , 1973 .

[6]  George L. Nemhauser,et al.  An Algorithm for the Line Balancing Problem , 1964 .

[7]  Linus Schrage,et al.  Dynamic Programming Solution of Sequencing Problems with Precedence Constraints , 1978, Oper. Res..

[8]  J. C. Picard,et al.  On the integer-valued variables in the linear vertex packing problem , 1977, Math. Program..

[9]  T. C. Hu.  Optimum Communication Spanning Trees , 1974, SIAM J. Comput..

[10]  D. Adolphson.  Optimal linear-ordering. , 1973 .

[11]  M. Balinski.  Notes—On a Selection Problem , 1970 .

[12]  H. W. Corley,et al.  Finding the n Most Vital Nodes in a Flow Network , 1974 .

[13]  M. Dessouky,et al.  Solving the Project Time/Cost Tradeoff Problem Using the Minimal Cut Concept , 1977 .

[14]  D. R. Fulkerson,et al.  Flows in Networks. , 1964 .

[15]  Leslie E. Trotter,et al.  Vertex packings: Structural properties and algorithms , 1975, Math. Program..

[16]  H. D. Ratliff,et al.  Minimum cuts and related problems , 1975, Networks.

[17]  J. Rhys.  A Selection Problem of Shared Fixed Costs and Network Flows , 1970 .

[18]  Lf McGinnis,et al.  The project coordinator's problem , 1978 .

[19]  S. Vajda,et al.  Integer Programming and Network Flows , 1970 .

[20]  M. Desu.  A Selection Problem , 1970 .