Skip to main content

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.
Back to article page

BMC Bioinformatics

ISSN: 1471-2105

Contact us