Isolating a Vertex via Lattices: Polytopes with Totally Unimodular Faces

@article{Gurjar2017IsolatingAV,
  title={Isolating a Vertex via Lattices: Polytopes with Totally Unimodular Faces},
  author={Rohit Gurjar and Thomas Thierauf and Nisheeth K. Vishnoi},
  journal={SIAM J. Comput.},
  year={2017},
  volume={50},
  pages={636-661}
}
We present a geometric approach towards derandomizing the Isolation Lemma by Mulmuley, Vazirani, and Vazirani. In particular, our approach produces a quasi-polynomial family of weights, where each weight is an integer and quasi-polynomially bounded, that can isolate a vertex in any 0/1 polytope for which each face lies in an affine space defined by a totally unimodular matrix. This includes the polytopes given by totally unimodular constraints and generalizes the recent derandomization of the… 

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The Matching Problem in General Graphs Is in Quasi-NC

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