An Efficient Dynamic Programming Algorithm and Implementation for RNA Secondary Structure Prediction

Abstract

RNA secondary structure prediction based on free energy rules for stacking and loop conformation remains a major computational method. The basic dynamic programming algorithm needs O(n4) time to calculate the minimum free energy for RNA secondary structure. To date, there are two variants for handling this problem: either the internal loops are bounded by a maximal size k giving a time complexity of O(n2*k2), or one uses the trick of Rune Lyngso, which makes use of the regularities of loop energies, to reduce time complexity to O(n3) without restriction. We propose a new dynamic programming algorithm for RNA secondary structure prediction by analyzing energy rules. Through only additional O(n) space, this algorithm eliminates redundant calculation in the energy calculation of internal loop with unrestricted/restricted size and reduces the time complexity of this part from O(n4) to O(n3), then the overall time complexity to O(n3).