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Table 1 The computational complexity of five specific counting problems under three different rearrangement models as described in details in the text.

From: Sampling and counting genome rearrangement scenarios

  Reversal DCJ SCJ
Pairwise rearrangement C: #P-complete C: #P-complete T: in FP [30]
  C: in FPRAS T: in FPRAS [25]  
Median T: not in FP T: not in FP T: in FP*
  T: not in FPRAS T: not in FPRAS  
Median scenario T: not in FP T: not in FP T: #P-complete[32]
  T: not in FPRAS T: not in FPRAS U: in/not in FPRAS
Tree labeling T: not in FP T: not in FP U: FP/#P-complete
  T: not in FPRAS T: not in FPRAS U: in/not in FPRAS
Tree scenario T: not in FP T: not in FP T: #P-complete[32]
  T: not in FPRAS T: not in FPRAS T: not in FPRAS [30]
  1. Notations: T: theorem, C: conjecture, U: unknown complexity, and there is no evidence to set up a conjecture favoring one of the possibilities. All theorems are referenced except: ‡: based on the fact that the corresponding optimization problem is NP-hard, *: proved in this paper. In all cases, "not in FP" should be considered under the assumption that P ≠ NP. Similarly, "not in FPRAS" should be considered under the assumption that RP ≠ NP.