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2 claims from 1 paper

1. Computer Science › Constraint Satisfaction and Optimization

   Cutting-plane algorithms and solution whitening for the vertex-cover problem

   Claussen and Hartmann · Physical review. E · 2022

   Using linear programming and cutting-plane methods on random graphs, the paper maps where vertex-cover solutions become incomplete, finds a further transition at c=2.90(2), and studies solution whitening.

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   1. Unchecked“While not generally complete solutions are obtained for graphs of arbitrarily high complexity, the CP approaches still advance the boundary in comparison to the pure SX algorithm, beyond the known replica-symmetry breaking (RSB) transition at c=e=2.718... .”
   2. UncheckedIn this study of the vertex-cover problem, whitening of solutions is affected only slightly, but measurably, by the replica-symmetry-breaking transition.“Inspection of the quantities related to clusters of white vertices reveals that whitening is affected, only slightly but measurably, by the RSB transition.”