The c-fragment longest arc-preserving common subsequence problem

Arc-annotated sequences are useful in representing the structural information of RNA and protein sequences. In particular, arc-annotated sequences are useful in describing the secondary and tertiary structures of RNA and protein sequences. Structure comparison for RNA and for protein sequences has become a central computational problem bearing many challenging computer science questions. The longest arc-preserving common subsequence problem has been introduced as a framework for studying the similarity of arc-annotated sequences. It is a sound and meaningful mathematical formalization of comparing the secondary structures of molecular sequences. In this paper, we consider two special cases of the longest arc-preserving common subsequence problem, efragment LAPCS (unlimited, plain), c-fragment LAPCS (unlimited, unlimited). In particular, we consider a parameterized version of the 1-fragment LAPCS (unlimited, plain) problem, parameterized by the length l of the desired subsequence. We show W[1]-completeness of the problem. Also, we describe an approach to solve c-fragment LAPCS (unlimited, unlimited). This approach is based on constructing logical models for the problem