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Journal of Combinatorial Optimization, 2006
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Mak, Vicky, Thomadsen, Tommy
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zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Mak, Vicky, Thomadsen, Tommy
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Chapter V Polyhedral combinatorics
Handbooks in Operations Research and Management Science, 1989Wr Pulleyblank
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Polyhedral Combinatorics in Combinatorial Optimization
Statistica Neerlandica, 1987Polyhedral combinatorics is a subarea of combinatorial optimization of increasing practical importance. It deals with the application of the theory of linear systems and linear algebra to combinatorial problems. The paper is not intended as a survey on polyhedral combinatorics but it reviews some of the main concepts and proof techniques.
Gerards, A.M.H., Kolen, A.W.J.
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Polyhedral Combinatorics and Neural Networks
Neural Computation, 1994The often disappointing performance of optimizing neural networks can be partly attributed to the rather ad hoc manner in which problems are mapped onto them for solution. In this paper a rigorous mapping is described for quadratic 0-1 programming problems with linear equality and inequality constraints, this being the most general class of problem ...
Andrew H. Gee, Richard W. Prager
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Polyhedral Combinatorics and Network Reliability
Mathematics of Operations Research, 1986This paper studies the reliability of systems comprised of variables which must satisfy a set of linear equalities and nonnegativity constraints, and which are subject to random failure. A major example, which will be given special emphasis, is the reachability (source-to-all connectedness reliability) problem for stochastic networks.
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Polyhedral combinatorics of multi-index axial transportation problems
European Journal of Operational Research, 2008For the \(p\)-index axial transportation polytope, the authors establish criteria for the minimum and maximum number of integer points and describe the class of polytopes for which the number of integer points coincides with the number of integer vertices.
Kravtsov, M. K., Lukshin, E. V.
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Information theory and polyhedral combinatorics
2015 53rd Annual Allerton Conference on Communication, Control, and Computing (Allerton), 2015The theory of extended formulations is concerned with the optimal polyhedral representation of a (combinatorial) optimization problem. In this context, information-theoretic methods recently gained significant attention as a convenient way to provide strong lower bounds on the size of such representations. We will provide an introduction to information-
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