A Complexity Dichotomy for Finding Disjoint Solutions of Vertex Deletion Problems

Michael R. Fellows, Jiong Guo, Hannes Moser, Rolf Niedermeier
2011 ACM Transactions on Computation Theory  
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:10.1145/1944857.1944860 fatcat:ci3bfpo4r5bulg3g4t4y2n2xly