Abstract
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.
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Alber, J., Gramm, J., Guo, J., Niedermeier, R.: Computing the Similarity of Two Sequences with Nested Arc Annotations. Theor. Comput. Sci. 312(2-3), 337–358 (2004)
Backofen, R., Landau, G.M., Möhl, M., Tsur, D., Weimann, O.: Fast RNA Structure Alignment for Crossing Input Structures. In: Proc. 20th CPM (2009)
Bafna, V., Muthukrishnan, S., Ravi, R.: Computing Similarity between RNA Strings. In: Galil, Z., Ukkonen, E. (eds.) CPM 1995. LNCS, vol. 937, pp. 1–16. Springer, Heidelberg (1995)
Bille, P., Gørtz, I.L.: The Tree Inclusion Problem: In Optimal Space and Faster. In: Caires, L., Italiano, G.F., Monteiro, L., Palamidessi, C., Yung, M. (eds.) ICALP 2005. LNCS, vol. 3580, pp. 66–77. Springer, Heidelberg (2005)
Blin, G., Fertin, G., Rizzi, R., Vialette, S.: What Makes the Arc-Preserving Subsequence Problem Hard? In: Proc. 5th ICCS, pp. 860–868 (2005)
Blin, G., Touzet, H.: How to Compare Arc-Annotated Sequences: The Alignment Hierarchy. In: Crestani, F., Ferragina, P., Sanderson, M. (eds.) SPIRE 2006. LNCS, vol. 4209, pp. 291–303. Springer, Heidelberg (2006)
Chen, W.: More Efficient Algorithm for Ordered Tree Inclusion. J. Algorithms 26, 370–385 (1998)
Damaschke, P.: A Remark on the Subsequence Problem for Arc-Annotated Sequences with Pairwise Nested Arcs. Inf. Process. Lett. 100(2), 64–68 (2006)
Evans, P.: Algorithms and Complexity for Annotated Sequence Analysis. PhD Thesis, University of Victoria (1999)
Gramm, J., Guo, J., Niedermeier, R.: Pattern Matching for Arc-Annotated Sequences. ACM Trans. Algorithms 2(1), 44–65 (2006); Announced at: Agrawal, M., Seth, A.K. (eds.) FSTTCS 2002. LNCS, vol. 2556, pp. 182–193. Springer, Heidelberg (2002)
Harel, D., Tarjan, R.E.: Fast Algorithms for Finding Nearest Common Ancestors. SIAM J. Comput. 13(2), 338–355 (1984)
Kida, T.: Faster Pattern Matching Algorithm for Arc-Annotated Sequences. In: Jantke, K.P., Lunzer, A., Spyratos, N., Tanaka, Y. (eds.) Federation over the Web. LNCS (LNAI), vol. 3847, pp. 25–39. Springer, Heidelberg (2006)
Kilpeläinen, P., Mannila, H.: Ordered and Unordered Tree Inclusion. SIAM J. Comput. 24, 340–356 (1995)
Lin, G., Chen, Z.-Z., Jiang, T., Wen, J.: The Longest Common Subsequence Problem for Sequences with Nested Arc Annotations. J. Comput. Syst. Sci. 65(3), 465–480 (2002)
Munro, I.: Tables. In: Chandru, V., Vinay, V. (eds.) FSTTCS 1996. LNCS, vol. 1180, pp. 37–42. Springer, Heidelberg (1996)
Vialette, S.: On the Computational Complexity of 2-Interval Pattern Matching Problems. Theor. Comput. Sci. 312(2-3), 223–249 (2004); Announced at CPM 2002
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Bille, P., Gørtz, I.L. (2010). Fast Arc-Annotated Subsequence Matching in Linear Space. In: van Leeuwen, J., Muscholl, A., Peleg, D., Pokorný, J., Rumpe, B. (eds) SOFSEM 2010: Theory and Practice of Computer Science. SOFSEM 2010. Lecture Notes in Computer Science, vol 5901. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11266-9_16
Download citation
DOI: https://doi.org/10.1007/978-3-642-11266-9_16
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-11265-2
Online ISBN: 978-3-642-11266-9
eBook Packages: Computer ScienceComputer Science (R0)