Pattern Matching for Arc-Annotated Sequences

Jens Gramm, Jiong Guo, Rolf Niedermeier

Abstract: A study of pattern matching for arc-annotated sequences is started. An O(nm) time algorithm is given to determine whether a length m sequence with nested arc annotations is an arc-preserving subsequence of a length n sequence with nested arc annotations, called APS(NESTED,NESTED). Arc-annotated sequences and, in particular, those with nested arc structure are motivated by applications in RNA structure comparison. Our algorithm can be used to accelerate a recent fixed-parameter algorithm for LAPCS(NESTED,NESTED) and generalizes results for ordered tree inclusion problems. In particular, the presented dynamic programming methodology implies a quadratic time algorithm for an open problem posed by Vialette.