Some Aspects of Duality in Combinatorial Optimization
The literature of combinatorial optimization, and of related fields such as graph theory. is replete with numerous examples of duality theorems and their applications: the Max-Flow Min-Cut Theorem, König-Egervary Theorem, Edmond’s Odd Set Covering Theorem, Hoffman’s Circulation Theorem, Minty’s Painting Theorem, Menger’s Theorem, Dilworth’s Theorem, etc. Our objective in this Chapter is to review a few of these duality results and to give some examples which may be convincing of the usefulness of duality concepts in problem formulation and solution.
KeywordsFeasible Solution Acyclic Directed Graph Duality Theorem Minimal Solution Graphic Duality
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