Important Separators and Parameterized Algorithms

The notion of "important separators" and bounding the number of such separators turned out to be a very useful technique in the design of fixed-parameter tractable algorithms for multi(way) cut problems. For example, the recent breakthrough result of Chen et al. [3] on the DIRECTED FEEDBACK VERTEX SET problem can be also explained using this notion. In my talk, I will overview combinatorial and algorithmic results that can be obtained by studying such separators.