Odd Minimum Cut Sets and $b$-Matchings Revisited

  • Authors:
  • Adam N. Letchford;Gerhard Reinelt;Dirk Oliver Theis

  • Affiliations:
  • A.N.Letchford@lancaster.ac.uk;Gerhard.Reinelt@informatik.uni-heidelberg.de;Dirk.Theis@ulb.ac.be

  • Venue:
  • SIAM Journal on Discrete Mathematics
  • Year:
  • 2008

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Abstract

The famous Padberg-Rao separation algorithm for $b$-matching polyhedra can be implemented to run in $\mathcal{O}(|V|^2|E|\log(|V|^2/|E|))$ time in the uncapacitated case, and in $\mathcal{O}(|V||E|^2\log(|V|^2/|E|))$ time in the capacitated case. We give a new and simple algorithm for the capacitated case which can be implemented to run in $\mathcal{O}(|V|^2|E|\log(|V|^2/|E|))$ time.