The Role of Ellipsoid Method for Complexity Analysis of Combinatorial Problems

  • Naum Z. Shor
Part of the Nonconvex Optimization and Its Applications book series (NOIA, volume 24)


Many combinatorial optimization problems can be reduced to the LP problems using the results from the field called “polyhedral combinatorics”. The main goal of polyhedral combinatorics is to represent the convex envelope of feasible points of the given combinatorial problem in the form of a system of linear equalities and inequalities. Obtained by this way LP problems often have an exponentially growing number of constraints. We know that at each step of ellipsoid method for LP we have to use no more than one constraint from the set of constraints which are not fulfilled at current point. In many cases the problem of finding such a constraint can be formulated in the form of a new combinatorial (in some sense polar to the original) optimization problem (so-called separation problem).


Convex Body Separation Problem Perfect Graph Ellipsoid Method Ellipsoid Algorithm 
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Copyright information

© Springer Science+Business Media Dordrecht 1998

Authors and Affiliations

  • Naum Z. Shor
    • 1
  1. 1.V.M. Glushkov Institute of CyberneticsUkrainian National Academy of SciencesKievUkraine

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