RNA molecules whose secondary structures contain similar substructures often have similar functions. Therefore, an important task in the study of RNA is to develop methods for discovering substructures in RNA secondary structures that occur frequently (also referred to as motifs). In this paper, we consider the problem of computing an optimal local alignment of two given labeled ordered forests F ₁ and F ₂. This problem asks for a substructure of F ₁ and a substructure of F ₂ that exhibit a high similarity. Since an RNA molecule's secondary structure can be represented as a labeled ordered forest, the problem we study has a direct application to finding potential motifs. We generalize the previously studied concept of a closed subforest to a gapped subforest and present the first algorithm for computing the optimal local gapped subforest alignment of F ₁ and F ₂. We also show that our technique can improve the time and space complexity of the previously most efficient algorithm for optimal local closed subforest alignment. Furthermore, we prove that a special case of our local gapped subforest alignment problem is equivalent to a problem known in the literature as the local sequence-structure alignment problem (lssa) and modify our main algorithm to obtain a much faster algorithm for lssa than the one previously proposed. An implementation of our algorithm is available at www.comp.nus.edu.sg/~bioinfo/LGSFAligner/. Its running time is significantly faster than the original lssa program.

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Local Gapped Subforest Alignment and Its Application in Finding RNA Structural Motifs