TY - GEN A1 - Schulz, Andreas S. A1 - Weismantel, Robert A1 - Ziegler, Günter M. T1 - 0/1-Integer Programming: Optimization and Augmentation are Equivalent N2 - {\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.} T3 - ZIB-Report - SC-95-08 Y1 - 1995 UR - https://opus4.kobv.de/opus4-zib/frontdoor/index/index/docId/174 UR - https://nbn-resolving.org/urn:nbn:de:0297-zib-1744 ER -