New approximation algorithms for RNA secondary structures prediction problems by local search

Aizhong Zhou, Haodi Feng, Jiong Guo, Haitao Jiang, Nan Liu, Binhai Zhu, Daming Zhu

Abstract: This paper investigates two combinatorial problems from RNA secondary structure prediction with arbitrary pseudoknots. Given a RNA sequence and a set of base pairs, two parallel and adjacent base pairs constitute a stacking. The Maximum Stacking Base Pairs problem (MSBP) aims at finding a maximum number of based pairs, all of which form stackings, while the Maximum Base Pair Stackings problem (MBPS) is to find a maximum number of stackings. Both problems are NP-hard. We present two new approximation algorithms for the two problems by local search methods. For MSBP, the approximation factor is improved from 52<math><mfrac is="true"><mrow is="true"><mn is="true">5</mn></mrow><mrow is="true"><mn is="true">2</mn></mrow></mfrac></math> to 73<math><mfrac is="true"><mrow is="true"><mn is="true">7</mn></mrow><mrow is="true"><mn is="true">3</mn></mrow></mfrac></math>; as for the MBPS, the approximation factor is improved from 83<math><mfrac is="true"><mrow is="true"><mn is="true">8</mn></mrow><mrow is="true"><mn is="true">3</mn></mrow></mfrac></math> to 52<math><mfrac is="true"><mrow is="true"><mn is="true">5</mn></mrow><mrow is="true"><mn is="true">2</mn></mrow></mfrac></math>.