The longest common subsequence problem for sequences with nested arc annotations (extended abstract)

Abstract

Arc-annotated sequences are useful in representing the structural information of RNA and protein sequences. The Longest ArcPreserving Common Subsequence (LAPCS) Problem has been introduced in [11] as a framework for studying the similarity of arc-annotated sequences. Several algorithmic and complexity results on the LAPCS problem have been presented in [11,17]. In this paper, we continue this line of research and present new algorithmic and complexity results on the LAPCS problem restricted to two nested arc-annotated sequences, denoted as LAPCS(nested, nested). The restricted problem is perhaps the most interesting variant of the LAPCS problem and has important applications in the comparison of RNA secondary and tertiary structures. Particularly, we prove that LAPCS(nested, nested) is NP-hard, which answers an open question in [11]. We then present a polynomial-time approximation scheme for LAPCS(nested, nested) with an additional cdiagonal restriction. An interesting special case, unary LAPCS(nested, nested), is also investigated. © 2011 Springer-Verlag Berlin Heidelberg.