Abstract
A genomic map is represented by a sequence of gene markers, and a gene marker can appear in several different genomic maps, in either positive or negative form. A strip (syntenic block) is a sequence of distinct markers that appears as subsequences in two or more maps, either directly or in reversed and negated form. Given two genomic maps G and H, the problem Maximal Strip Recovery (MSR) is to find two subsequences G′ and H′ of G and H, respectively, such that the total length of disjoint strips in G′ and H′ is maximized. Previously only a heuristic was provided for this problem, which does not guarantee finding the optimal solution, and it was unknown whether the problem is NP-complete or polynomially solvable. In this paper, we develop a factor-4 polynomial-time approximation algorithm for the problem, and show that several close variants of the problem are intractable.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Bar-Yehuda, R., Halldórsson, M.M. (Selfi) Naor, J., Shachnai, H., Shapira, I.: Scheduling split intervals. SIAM Journal on Computing 36, 1–15 (2006)
Blin, G., Fertin, G., Vialette, S.: Extracting constrained 2-interval subsets in 2-interval sets. Theoretical Computer Science 385, 241–263 (2007)
Chen, Z., Fu, B., Yang, B., Xu, J., Zhao, Z., Zhu, B.: Non-breaking similarity of genomes with gene repetitions. In: Ma, B., Zhang, K. (eds.) CPM 2007. LNCS, vol. 4580, pp. 119–130. Springer, Heidelberg (2007)
Chen, J., Huang, X., Kanj, I., Xia, G.: Linear FPT reductions and computational lower bounds. In: Proceedings of the 36th ACM Symposium on Theory of Computing (STOC 2004), pp. 212–221 (2004)
Chen, E., Yang, L., Yuan, H.: Improved algorithms for largest cardinality 2-interval pattern problem. Journal of Combinatorial Optimization 13, 263–275 (2007)
Choi, V., Zheng, C., Zhu, Q., Sankoff, D.: Algorithms for the extraction of synteny blocks from comparative maps. In: Proceedings of the 7th International Workshop on Algorithms in Bioinformatics (WABI 2007), pp. 277–288 (2007)
Crochemore, M., Hermelin, D., Landau, G.M., Rawitz, D., Vialette, S.: Approximating the 2-interval pattern problem. In: Brodal, G.S., Leonardi, S. (eds.) ESA 2005. LNCS, vol. 3669, pp. 426–437. Springer, Heidelberg (2005)
Downey, R., Fellows, M.: Parameterized Complexity. Springer, Heidelberg (1999)
Jiang, M.: A 2-approximation for the preceding-and-crossing structured 2-interval pattern problem. Journal of Combinatorial Optimization 13, 217–221 (2007)
Jiang, M.: Improved approximation algorithms for predicting RNA secondary structures with arbitrary pseudoknots. In: Kao, M.-Y., Li, X.-Y. (eds.) AAIM 2007. LNCS, vol. 4508, pp. 399–410. Springer, Heidelberg (2007)
Jiang, M.: A PTAS for the weighted 2-interval pattern problem over the preceding-and-crossing model. In: Dress, A.W.M., Xu, Y., Zhu, B. (eds.) COCOA. LNCS, vol. 4616, pp. 378–387. Springer, Heidelberg (2007)
Lyngsø, R.B.: Complexity of pseudoknot prediction in simple models. In: Díaz, J., Karhumäki, J., Lepistö, A., Sannella, D. (eds.) ICALP 2004. LNCS, vol. 3142, pp. 919–931. Springer, Heidelberg (2004)
Schaefer, T.: The complexity of satisfiability problem. In: Proceedings of the 10th ACM Symposium on Theory of Computing (STOC 1978), pp. 216–226 (1978)
Vialette, S.: On the computational complexity of 2-interval pattern matching problems. Theoretical Computer Science 312, 223–249 (2004)
Watterson, G., Ewens, W., Hall, T., Morgan, A.: The chromosome inversion problem. Journal of Theoretical Biology 99, 1–7 (1982)
Zheng, C., Zhu, Q., Sankoff, D.: Removing noise and ambiguities from comparative maps in rearrangement analysis. IEEE/ACM Transactions on Computational Biology and Bioinformatics 4, 515–522 (2007)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Chen, Z., Fu, B., Jiang, M., Zhu, B. (2008). On Recovering Syntenic Blocks from Comparative Maps. In: Yang, B., Du, DZ., Wang, C.A. (eds) Combinatorial Optimization and Applications. COCOA 2008. Lecture Notes in Computer Science, vol 5165. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-85097-7_30
Download citation
DOI: https://doi.org/10.1007/978-3-540-85097-7_30
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-85096-0
Online ISBN: 978-3-540-85097-7
eBook Packages: Computer ScienceComputer Science (R0)