Solution bases of multiterminal cut problems
Mathematics of Operations Research
Network programming
Network flows: theory, algorithms, and applications
Network flows: theory, algorithms, and applications
Integer solution to synthesis of communication networks
Mathematics of Operations Research
Generalizing the all-pairs min cut problem
Discrete Mathematics
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Multiroute flow problem
Multi-terminal multipath flows: synthesis
Discrete Applied Mathematics
Operations Research Letters
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In the context of q-route flows in an undirected network with non-negative edge capacities, for integer values of q=2, we consider two problems of both theoretical and practical interest. The first problem focuses on investigating the existence and construction of a cut-tree. For q=2, we show that a cut-tree always exists and can be constructed in strongly polynomial time. However, for q=3, in general, a cut-tree does not exist and we establish this through a counter-example. The second problem addresses the issue of checking if a given matrix R is 2-realizable-that is, checking if there exists an undirected, simple network with non-negative edge capacities such that the non-diagonal elements of R are precisely the maximum 2-route flow values between corresponding pairs of nodes in the network. We provide a complete characterization of 2-realizable matrices and using this characterization, we prove that the problem of testing if a given matrix is 2-realizable is, in general, NP-complete.