2 research outputs found
Fast Arc-Annotated Subsequence Matching in Linear Space
An arc-annotated string is a string of characters, called bases, augmented
with a set of pairs, called arcs, each connecting two bases. Given
arc-annotated strings and the arc-preserving subsequence problem is to
determine if can be obtained from by deleting bases from . Whenever
a base is deleted any arc with an endpoint in that base is also deleted.
Arc-annotated strings where the arcs are ``nested'' are a natural model of RNA
molecules that captures both the primary and secondary structure of these. The
arc-preserving subsequence problem for nested arc-annotated strings is basic
primitive for investigating the function of RNA molecules. Gramm et al. [ACM
Trans. Algorithms 2006] gave an algorithm for this problem using time
and space, where and are the lengths of and , respectively. In
this paper we present a new algorithm using time and space,
thereby matching the previous time bound while significantly reducing the space
from a quadratic term to linear. This is essential to process large RNA
molecules where the space is likely to be a bottleneck. To obtain our result we
introduce several novel ideas which may be of independent interest for related
problems on arc-annotated strings.Comment: To appear in Algoritmic