Finding small separators in linear time via treewidth reduction

@article{Marx2013FindingSS,
  title={Finding small separators in linear time via treewidth reduction},
  author={D{\'a}niel Marx and Barry O'Sullivan and Igor Razgon},
  journal={ACM Trans. Algorithms},
  year={2013},
  volume={9},
  pages={30:1-30:35}
}
We present a method for reducing the treewidth of a graph while preserving all of its minimal <i>s</i>-<i>t</i> separators up to a certain fixed size <i>k</i>. This technique allows us to solve <i>s</i>-<i>t</i> <scp>Cut</scp> and <scp>Multicut</scp> problems with various additional restrictions (e.g., the vertices being removed from the graph form an independent set or induce a connected graph) in linear time for every fixed number <i>k</i> of removed vertices. Our results have applications… CONTINUE READING