Fig. 1

Histogram of treewidth values over all RNA-only structures in the PDB database [24]. The data consists of 5 760 non-redundant graphs, each corresponding to a “chain” of a PDB entity. The nucleotide chains and their base pairs were extracted using the DSSR tool [25]. On each of these graphs, 4 standard treewidth heuristics from the LibTW library [26] (min-degree, min-fill-in, lex-BFS, max-cardinality-search) were launched, and the best width result was selected. Even if these heuristics reputedly tend to yield results close to the optimal, these results are still upper bounds. For each individual structure, the actual treewidth value may be lower. Depending on whether non-canonical base pairs are taken into account (right) or not (left), the proportion of structures having a width \(\ge 4\) ranges from  50 to \(70\%\). For such values, the complexity of structure-sequence alignment (\(O(n\cdot m^{tw+1})\)) becomes prohibitive. It is also worth noting that only pseudo-knotted structures may have a treewidth \(\ge 3\)