Arc-preserving subsequences of arc-annotated sequences

Arc-annotated sequences are useful in representing the structural information of RNA and protein sequences. The longest arc-preserving common subsequence problem has been introduced as a framework for studying the similarity of arc-annotated sequences. In this paper, we consider arc-annotated sequences with various arc structures. We consider the longest arc preserving common subsequence problem. In particular, we show that the decision version of the 1-fragment LAPCS(crossing,chain) and the decision version of the 0-diagonal LAPCS(crossing,chain) are NP-complete for some fixed alphabet Σ such that |Σ| = 2. Also we show that if |Σ| = 1, then the decision version of the 1-fragment LAPCS(unlimited, plain) and the decision version of the 0-diagonal LAPCS(unlimited, plain) are NP-complete.