Polytopes, graphs and optimisation
Polytopes, graphs and optimisation
Theory of linear and integer programming
Theory of linear and integer programming
Combinatorial optimization: algorithms and complexity
Combinatorial optimization: algorithms and complexity
Network flows: theory, algorithms, and applications
Network flows: theory, algorithms, and applications
Computational Optimization and Applications
An O(n2(m + Nlog n)log n) min-cost flow algorithm
Journal of the ACM (JACM)
Beyond the flow decomposition barrier
Journal of the ACM (JACM)
Computers and Intractability; A Guide to the Theory of NP-Completeness
Computers and Intractability; A Guide to the Theory of NP-Completeness
Extracting pure network submatrices in linear programs using signed graphs
Discrete Applied Mathematics
Multiindex resource distributions for hierarchical systems
Automation and Remote Control
Graphs of transportation polytopes
Journal of Combinatorial Theory Series A
Multi-index transport problems with decomposition structure
Automation and Remote Control
Multiindex transportation problems with 2-embedded structure
Automation and Remote Control
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This paper deals with solutions of multi-index linear programs of the transportation type. The approach based on the analysis of reducibility of multi-index transportation problems to flow algorithms is taken as the main technical tool. Sufficient conditions of reducibility are proposed, which are based on the notion of nesting for the set of problem constraints. It is shown that these conditions are necessary and sufficient for reducibility of three-index problems; otherwise, the well-know hypothesis on the non-equivalence of the classes P and NP is wrong.