Rank Lower Bounds for Generic Cutting-Plane Proof Systems

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  • Date/Time:
    • Tuesday February 1, 2011
      10:00 am - 11:00 am
  • Location: ISyE Executive classroom
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Summary Sentence: Rank Lower Bounds for Generic Cutting-Plane Proof Systems

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TITLE:  Rank Lower Bounds for Generic Cutting-Plane Proof Systems

SPEAKER:  Sebastian Pokutta - faculty candidate

ABSTRACT:

We introduce a natural abstraction of cutting-plane proof systems, which subsumes well-known operators such as Gomory-Chvátal, lift-and-project, Sherali-Adams, Lovász-Schrijver, and split cuts. We exhibit a family of polytopes without integral points contained in the n-dimensional 0/1-cube that has rank Omega(n/ log n) for any proof system in our class. In fact, we show that whenever a specific cutting-plane based proof system has (maximal) rank n
on a particular family of instances, then any cutting-plane proof system in our class has rank Omega(n/ log n) for this family. We also construct a new cutting-plane proof system that has worst-case rank O(n/ log n) for any polytope without integral points, implying that the new universal lower bound is virtually tight.
(joint work with Andreas S. Schulz)

 


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H. Milton Stewart School of Industrial and Systems Engineering (ISYE)

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  • Created By: Anita Race
  • Workflow Status: Published
  • Created On: Jan 5, 2011 - 6:51am
  • Last Updated: Oct 7, 2016 - 9:53pm