Improved Approximation Algorithm for the Maximum Base Pair Stackings Problem in RNA Secondary Structures Prediction

Abstract

We investigate the maximum base pair stackings problem from RNA Secondary Structures prediction in this paper. Previously, Ieong et al. defined a basic version of this maximum base pair stackings problem as: given an RNA sequence, finding a set of base pairs to constitute a maximum number of stackings, and proved it to be NP-hard, where the base pairs are default under some biology principle and are given implicitly. Jiang proposed a generalized version of this problem, where the candidate base pairs are given explicitly as input and presented an approximation algorithm with a factor 8/3. In this paper, we present a new approximation algorithm for the generalized maximum base pair stackings problem by a two-stage local search method, improving the approximation factor from 8/3+ varepsilon to 5/2. Since we adopt only two basic local operations, 1-substitutions and 2-substitutions, during the local improvement stage, the time complexity can be bounded by O(n^7), much faster than the previous approximation algorithms.