Faster Algorithms for RNA-folding using the Four-Russians method

TL;DR

This paper introduces simplified and efficient algorithms for RNA folding using the Four-Russians method, achieving significant speedups over previous algorithms through preprocessing and parallelization techniques.

Contribution

The authors present a simplified two-vector preprocessing method and parallel algorithms that improve RNA folding computation times, with practical implementation details and speed comparisons.

Findings

The two-vector method simplifies the Four-Russians-based RNA folding algorithm.

Parallel algorithm reduces the time complexity to O(n^2 / log n).

Serial algorithms outperform previous methods by factors of 3 to 20.

Abstract

The secondary structure that maximizes the number of non-crossing matchings between complimentary bases of an RNA sequence of length n can be computed in O(n^3) time using Nussinov's dynamic programming algorithm. The Four-Russians method is a technique that will reduce the running time for certain dynamic programming algorithms by a multiplicative factor after a preprocessing step where solutions to all smaller subproblems of a fixed size are exhaustively enumerated and solved. Frid and Gusfield designed an O(\frac{n^3}{\log n}) algorithm for RNA folding using the Four-Russians technique. In their algorithm the preprocessing is interleaved with the algorithm computation. (Algo. Mol. Biol., 2010). We simplify the algorithm and the analysis by doing the preprocessing once prior to the algorithm computation. We call this the two-vector method. We also show variants where instead of exhaustive preprocessing, we only solve the subproblems encountered in the main algorithm once and memoize the results. We give a simple proof of correctness and explore the practical advantages over the earlier method. The Nussinov algorithm admits an O(n^2) time parallel algorithm. We show a parallel algorithm using the two-vector idea that improves the time bound to O(\frac{n^2}{log n}). We discuss the organization of the data structures to exploit coalesced memory access for fast running times. The ideas to organize the data structures also help in improving the running time of the serial algorithms. For sequences of length up to 6000 bases the parallel algorithm takes only about 2.5 seconds and the two-vector serial method takes about 57 seconds on a desktop and 15 seconds on a server. Among the serial algorithms, the two-vector and memoized versions are faster than the Frid-Gusfield algorithm by a factor of 3, and are faster than Nussinov by up to a factor of 20.