Predicting RNA Secondary Structures with Arbitrary Pseudoknots by Maximizing the Number of Stacking Pairs

Samuel Ieong, Ming-Yang Kao, Tak Wah Lam, Wing Kin Sung, Siu Ming Yiu*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

54 Scopus citations


The paper investigates the computational problem of predicting RNA secondary structures. The general belief is that allowing pseudoknots makes the problem hard. Existing polynomial-time algorithms are heuristic algorithms with no performance guarantee and can handle only limited types of pseudoknots. In this paper, we initiate the study of predicting RNA secondary structures with a maximum number of stacking pairs while allowing arbitrary pseudoknots. We obtain two approximation algorithms with worst-case approximation ratios of 1/2 and 1/3 for planar and general secondary structures, respectively. For an RNA sequence of n bases, the approximation algorithm for planar secondary structures runs in O(n3) time while that for the general case runs in linear time. Furthermore, we prove that allowing pseudoknots makes it NP-hard to maximize the number of stacking pairs in a planar secondary structure. This result is in contrast with the recent NP-hard results on psuedoknots which are based on optimizing some general and complicated energy functions.

Original languageEnglish (US)
Pages (from-to)981-995
Number of pages15
JournalJournal of Computational Biology
Issue number6
StatePublished - 2003


  • Approximation algorithms
  • Computational complexity
  • Pseudoknots
  • RNA secondary structures
  • Stacking pairs

ASJC Scopus subject areas

  • Modeling and Simulation
  • Molecular Biology
  • Genetics
  • Computational Mathematics
  • Computational Theory and Mathematics


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