The longest common subsequence problem for arc-annotated sequences

Abstract

Arc-annotated sequences are useful in representing the structural information of RNA and protein sequences. The Longest Arc-Preserving Common Subsequence (LAPCS) problem has recently been introduced in [P.A. Evans, Algorithms and complexity for annotated sequence analysis, PhD Thesis, University of Victoria, 1999; P.A. Evans, Finding common subsequences with arcs and pseudoknots, in: Proceedings of 10th Annual Symposium on Combinatorial Pattern Matching (CPM'99), in: Lecture Notes in Comput. Sci., vol. 1645, 1999, pp. 270–280] as a framework for studying the similarity of arc-annotated sequences. In this paper, we consider arc-annotated sequences with various arc structures and present some new algorithmic and complexity results on the LAPCS problem. Some of our results answer an open question in [P.A. Evans, Algorithms and complexity for annotated sequence analysis, PhD Thesis, University of Victoria, 1999; P.A. Evans, Finding common subsequences with arcs and pseudoknots, in: Proceedings of 10th Annual Symposium on Combinatorial Pattern Matching (CPM'99), in: Lecture Notes in Comput. Sci., vol. 1645, 1999, pp. 270–280] and some others improve the hardness results in [P.A. Evans, Algorithms and complexity for annotated sequence analysis, PhD Thesis, University of Victoria, 1999; P.A. Evans, Finding common subsequences with arcs and pseudoknots, in: Proceedings of 10th Annual Symposium on Combinatorial Pattern Matching (CPM'99), in Lecture Notes in Comput. Sci., vol. 1645, 1999, pp. 270–280].