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0/1-Integer programming: Optimization and Augmentation are equivalent

Session 8. Chair: Michael Juenger

Part of the Lecture Notes in Computer Science book series (LNCS,volume 979)

Abstract

For every family of sets \(\mathcal{F} \subseteq \{ 0,1\} ^n\)the following problems are strongly polynomial time equivalent: given a feasible point x0\(\mathcal{F}\)and a linear objective function c ∈ ℤ n,

  • find a feasible point x * \(\mathcal{F}\)that maximizes c x (Optimization),

  • find a feasible point x new\(\mathcal{F}\)with cx new > cx 0 (Augmentation), and

  • find a feasible point xnew\(\mathcal{F}\)with cx new > c x 0 such that x newx 0 is “irreducible” (Irreducible Augmentation).

This generalizes results and techniques that are well known for 0/1-integer programming problems that arise from various classes of combinatorial optimization problems.

Keywords

  • Polynomial Time
  • Polynomial Time Algorithm
  • Feasible Point
  • Linear Objective Function
  • Augmentation Problem

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Andreas S. Schulz has been supported by the graduate school “Algorithmische Diskrete Mathematik”. The graduate school “Algorithmische Diskrete Mathematik” is supported by the Deutsche Forschungsgemeinschaft (DFG), grant We 1265/2-1.

Günter M. Ziegler acknowledges support by a DFG Gerhard-Hess-Forschungsförderungspreis.

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© 1995 Springer-Verlag Berlin Heidelberg

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Schulz, A.S., Weismantel, R., Ziegler, G.M. (1995). 0/1-Integer programming: Optimization and Augmentation are equivalent. In: Spirakis, P. (eds) Algorithms — ESA '95. ESA 1995. Lecture Notes in Computer Science, vol 979. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60313-1_164

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  • DOI: https://doi.org/10.1007/3-540-60313-1_164

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