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Motivation: Predicting the secondary structure of an RNA sequence is usefulin many applications. Existing algorithms (based on dynamic programming) sufferfrom a major limitation: their runtimes scale cubically with the RNA length,and this slowness limits their use in genome-wide applications.  Results: We present a novel alternative $O(n^3)$-time dynamic programmingalgorithm for RNA folding that is amenable to heuristics that make it run in$O(n)$ time and $O(n)$ space, while producing a high-quality approximation tothe optimal solution. Inspired by incremental parsing for context-free grammarsin computational linguistics, our alternative dynamic programming algorithmscans the sequence in a left-to-right (5'-to-3') direction rather than in abottom-up fashion, which allows us to employ the effective beam pruningheuristic. Our work, though inexact, is the first RNA folding algorithm toachieve linear runtime (and linear space) without imposing constraints on theoutput structure. Surprisingly, our approximate search results in even higheroverall accuracy on a diverse database of sequences with known structures. Moreinterestingly, it leads to significantly more accurate predictions on thelongest sequence families in that database (16S and 23S Ribosomal RNAs), aswell as improved accuracies for long-range base pairs (500+ nucleotides apart),both of which are well known to be challenging for the current models.  Availability: Our source code is available athttps://github.com/LinearFold/LinearFold, and our webserver is athttp://linearfold.org (sequence limit: 100,000nt).

LinearFold: linear-time approximate RNA folding by 5'-to-3' dynamic programming and beam search