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0/1-Integer Programming: Optimization and Augmentation are Equivalent (1995)

Schulz, Andreas S. ; Weismantel, Robert ; Ziegler, Günter M.

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Publikationsdatum: 2014-02-26

Beschreibung: {\def\xnew{x^{\mbox{\tiny new}}}\def\Z{{{\rm Z}\!\! Z}}For every fixed set ${\cal F}\subseteq\{0,1\}^n$ the following problems are strongly polynomial time equivalent: given a feasible point $x\in\cal F$ and a linear objective function $c\in\Z^n$, \begin{itemize} \item find a feasible point $x^*\in\cal F$ that maximizes $cx$ (Optimization), \item find a feasible point $\xnew\in\cal F$ with $c\xnew〉cx$ (Augmentation), and \item find a feasible point $\xnew\in\cal F$ with $c\xnew〉cx$ such that $\xnew-x$ is ``irreducible''\\(Irreducible Augmentation). \end{itemize} This generalizes results and techniques that are well known for $0/1$--integer programming problems that arise from various classes of combinatorial optimization problems.}

Schlagwort(e): ddc:000

Sprache: Englisch

Materialart: reportzib , doc-type:preprint

Format: application/postscript

Format: application/pdf

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