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Submodular Functions

  • Martin Grötschel
  • László Lovász
  • Alexander Schrijver
Chapter
  • 1.3k Downloads
Part of the Algorithms and Combinatorics book series (AC, volume 2)

Abstract

The concept of a submodular function in discrete optimization appears to be in several respects analogous to that of a convex function in continuous optimization. In many combinatorial theorems and problems, submodularity is involved, in one form or another, and submodularity often plays an essential role in a proof or an algorithm. Moreover, analogous to the fast methods for convex function minimization, it turns out that submodular functions can also be minimized fast, viz. in polynomial time. However, the only method known for this is, as yet, the ellipsoid method.

Keywords

Polynomial Time Greedy Algorithm Rank Function Submodular Function Ellipsoid Method 
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.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • Martin Grötschel
    • 1
    • 2
  • László Lovász
    • 3
    • 4
  • Alexander Schrijver
    • 5
    • 6
  1. 1.Konrad-Zuse-Zentrum für Informationstechnik BerlinBerlinGermany
  2. 2.Fachbereich MathematikTechnische Universität BerlinBerlinGermany
  3. 3.Department of Computer ScienceEötvös Loránd UniversityBudapestHungary
  4. 4.Department of MathematicsYale UniversityNew HavenUSA
  5. 5.CWI (Center for Mathematics and Computer Science)AmsterdamThe Netherlands
  6. 6.Department of MathematicsUniversity of AmsterdamAmsterdamThe Netherlands

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