A Complexity Dichotomy for Finding Disjoint Solutions of Vertex Deletion Problems [chapter]

Michael R. Fellows, Jiong Guo, Hannes Moser, Rolf Niedermeier
2009 Lecture Notes in Computer Science  
We investigate the computational complexity of a general "compression task" centrally occurring in the recently developed technique of iterative compression for exactly solving NP-hard minimization problems. The core issue (particularly but not only motivated by iterative compression) is to determine the computational complexity of, given an already inclusion-minimal solution for an underlying (typically NPhard) vertex deletion problem in graphs, to find a better disjoint solution. The
more » ... y of this task is so far lacking a systematic study. We consider a large class of vertex deletion problems on undirected graphs and show that, except for few cases which are polynomial-time solvable, the others are NP-complete. This class includes problems such as Vertex Cover (here the corresponding compression task is decidable in polynomial time) or Undirected Feedback Vertex Set (here the corresponding compression task is NP-complete).
doi:10.1007/978-3-642-03816-7_28 fatcat:3gifzkyfkbaw3gvaedx5cynmda