Fast algorithms for finding nearest common ancestors
SIAM Journal on Computing
Ordered and Unordered Tree Inclusion
SIAM Journal on Computing
More efficient algorithm for ordered tree inclusion
Journal of Algorithms
The longest common subsequence problem for sequences with nested arc annotations
Journal of Computer and System Sciences - Computational biology 2002
Proceedings of the 16th Conference on Foundations of Software Technology and Theoretical Computer Science
Pattern Matching for Arc-Annotated Sequences
FST TCS '02 Proceedings of the 22nd Conference Kanpur on Foundations of Software Technology and Theoretical Computer Science
Algorithms and complexity for annotated sequence analysis
Algorithms and complexity for annotated sequence analysis
On the computational complexity of 2-interval pattern matching problems
Theoretical Computer Science
Computing the similarity of two sequences with nested arc annotations
Theoretical Computer Science
A remark on the subsequence problem for arc-annotated sequences with pairwise nested arcs
Information Processing Letters
Fast RNA Structure Alignment for Crossing Input Structures
CPM '09 Proceedings of the 20th Annual Symposium on Combinatorial Pattern Matching
The tree inclusion problem: in optimal space and faster
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
How to compare arc-annotated sequences: the alignment hierarchy
SPIRE'06 Proceedings of the 13th international conference on String Processing and Information Retrieval
Faster pattern matching algorithm for arc-annotated sequences
Proceedings of the 2005 international conference on Federation over the Web
What makes the arc-preserving subsequence problem hard?
ICCS'05 Proceedings of the 5th international conference on Computational Science - Volume Part II
Hi-index | 0.00 |
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 P and Q the arc-preserving subsequence problem is to determine if P can be obtained from Q by deleting bases from Q. 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 O(nm) time and space, where m and n are the lengths of P and Q, respectively. In this paper we present a new algorithm using O(nm) time and O(n + m) 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 a 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.