The Computation of the Barrier Tree for BHG of RNA Folding Structure

The number of different RNA secondary structures makes it impossible to enumerate the entire landscape except for short RNA sequences, so one has to resort to coarse-grained approximations. The landscape of the barrier tree encodes the local minima and their connecting energy barriers. The idea that it elucidates the basin structure of a landscape by means of a barrier tree has been developed independently in different contexts. The exact computation of barrier trees in general requires the enumeration of the landscape. There are many methods to compute the barrier tree, such as the Euclidean metric and the Huffman tree. We adopt the idea of the Huffman tree to compute the barrier tree, the thought is that we can see the every node in the tree as a separate tree, and then choose the smallest roots to merge into a tree. This process will not end until only one tree left in the forest.