![](bg6.png)
The minimum free energy of the optimal structure
for the whole RNA sequence is the minimum value
of {min
x
{S
odd
D
(1, x, x + 1, n)}, min
y<x
3
{S
even
D
(1, y, y +
1, x
3
, x
3
)}}.
From the real data, the distance between x
3
and
the end of the sequence is usually bounded by a small
constant, so we assume that the number of different
x
3
values we need to consider is only a small con-
stant. The time complexity of the above algorithm is
O(m
4
). The memory complexity of the algorithm is
also O(m
4
) .
5 CONCLUSIONS
In this paper, we consider a new class of pseudoknots
which include more complicated structures that none
of the existing algorithms can handle. We then pro-
vide an O(m
4
) time algorithm for predicting these
a structure of degree 4 with minimum free energy
which already covers all known secondary structures
of this class in existing databases. We implemented
our algorithm and the running time is reasonable,
which takes about 70sec for a RNA of length about
100 and about 3 times faster than the one in (Rivas
and Eddy, 1999). We will evaluate the accuracy of
the predicted structures once we can locate a set of
appropriate parameters for the energy model. In fact,
there are not many known RNAs with simple non-
standard pseudoknots. One of the reasons may be due
to the limitation of existing computational prediction
tools. With our algorithm, we may be able to pre-
dict more RNAs with such a structure for follow-up
verification. Although there are no other more com-
plicated known pseudoknot structures, there is a high
chance that there exist novelRNAs with more compli-
cated structures, so designing efficient prediction al-
gorithms for more complicated pseudoknot structures
remains an important open problem.
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