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Table 1 Computational complexity of the existing and proposed methods are summarized

From: RintC: fast and accuracy-aware decomposition of distributions of RNA secondary structures with extended logsumexp

 

RintW, time

RintC (proposed), time

preprocessing

O(N2)

O(N2)

main calculation

O(N5/U)

O(N2W3/U)

postprocessing (DFT)

O(N4/U)

O(N3W/U)

postprocessing (FFT)

O(N3logN/U)

O(N2WlogN/U)

total (DFT)

O(N5/U)

O(N2W(W2+N)/U)

total (FFT)

O(N5/U)

O(N2W(W2+logN)/U)

 

RintW, space

RintC (proposed), space

preprocessing

O(N2)

O(N2)

main calculation

O(N3U)

O(N2WU)

postprocessing (DFT)

O(NU)

O(NU)

postprocessing (FFT)

O(NU)

O(NU)

total (DFT)

O(N3U)

O(N2WU)

total (FFT)

O(N3U)

O(N2WU)

  1. N = sequence length. W = maximum-span. Note that Hmax≤N and W≤N always holds. U = degree of parallelism