Multi-terminal maximum flows in node-capacitated networks
Discrete Applied Mathematics
Solution bases of multiterminal cut problems
Mathematics of Operations Research
Counterexamples for Directed and Node Capacitated Cut-Trees
SIAM Journal on Computing
Generalizing the all-pairs min cut problem
Discrete Mathematics
Compact Representations of Cuts
SIAM Journal on Discrete Mathematics
The Number of Solutions Sufficient for Solving a Family of Problems
Mathematics of Operations Research
An algorithm for computing maximum solution bases
Operations Research Letters
| Hi-index | 0.04 |
Given a graph G=(V,E) with a cost function c(S)=0@?S@?V, we want to represent all possible min-cut values between pairs of vertices i and j. We consider also the special case with an additive cost c where there are vertex capacities c(v)=0@?v@?V, and for a subset S@?V, c(S)=@?"v"@?"Sc(v). We consider two variants of cuts: in the first one, separation, {i} and {j} are feasible cuts that disconnect i and j. In the second variant, vertex-cut, a cut-set that disconnects i from j does not include i or j. We consider both variants for undirected and directed graphs. We prove that there is a flow-tree for separations in undirected graphs. We also show that a compact representation does not exist for vertex-cuts in undirected graphs, even with additive costs. For directed graphs, a compact representation of the cut-values does not exist even with additive costs, for neither the separation nor the vertex-cut cases.