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

  • Andreas S. Schulz
  • Robert Weismantel
  • Günter M. Ziegler
Session 8. Chair: Michael Juenger

DOI: 10.1007/3-540-60313-1_164

Volume 979 of the book series Lecture Notes in Computer Science (LNCS)
Cite this paper as:
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

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

  • find a feasible point xnew\(\mathcal{F}\)with cxnew > cx0 (Augmentation), and

  • find a feasible point xnew\(\mathcal{F}\)with cxnew > c x0 such that xnewx0 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.

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Copyright information

© Springer-Verlag 1995

Authors and Affiliations

  • Andreas S. Schulz
    • 1
  • Robert Weismantel
    • 2
  • Günter M. Ziegler
    • 3
  1. 1.Technische Universität Berlin, Fachbereich Mathematik (MA 6-1)BerlinGermany
  2. 2.Konrad-Zuse-Zentrum für Informationstechnik BerlinBerlinGermany
  3. 3.Technische Universität Berlin, Fachbereich Mathematik (MA 6-1)BerlinGermany