Abstract
Given two genomic maps G and H represented by a sequence of n gene markers, a strip (syntenic block) is a sequence of distinct markers of length at least two which appear as subsequences in the input maps, either directly or in reversed and negated form. 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 (i.e., conversely, the complement of the problem CMSR is to minimize the number of markers deleted to have a feasible solution). Recently, both MSR and its complement are shown to be NP-complete. A factor-4 approximation is known for the MSR problem and an FPT algorithm is known for the CMSR problem which runs in O(23.61k n + n 2) time (where k is the minimum number of markers deleted). We show in this paper that there is a factor-3 asymptotic approximation for CMSR and there is an FPT algorithm which runs in O(3k n + n 2) time for CMSR, significantly improving the previous bound.
This is a preview of subscription content, log in via an institution to check access.
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
Bar-Yehuda, R., Halldórsson, M.M., Naor, J.(S.), Shachnai, H., Shapira, I.: Scheduling split intervals. SIAM Journal on Computing 36, 1–15 (2006)
Bulteau, L., Fertin, G., Rusu, I.: Maximal strip recovery problem with gaps: hardness and approximation algorithms. In: Dong, Y., Du, D.-Z., Ibarra, O. (eds.) ISAAC 2009. LNCS, vol. 5878, pp. 710–719. Springer, Heidelberg (2009)
Butman, A., Hermelin, D., Lewenstein, M., Rawitz, D.: Optimization problems in multiple-interval graphs. In: Proceedings of the 18th ACM-SIAM Symposium on Discrete Algorithms (SODA 2007), pp. 268–277 (2007)
Chen, Z., Fu, B., Jiang, M., Zhu, B.: On recovering syntenic blocks from comparative maps. Journal of Combinatorial Optimization 18, 307–318 (2009)
Choi, V., Zheng, C., Zhu, Q., Sankoff, D.: Algorithms for the extraction of synteny blocks from comparative maps. In: Giancarlo, R., Hannenhalli, S. (eds.) WABI 2007. LNCS (LNBI), vol. 4645, pp. 277–288. Springer, Heidelberg (2007)
Downey, R., Fellows, M.: Parameterized Complexity. Springer, Heidelberg (1999)
Jiang, H., Zhu, B.: Weak kernels. ECCC Report, TR10-005 (May 2010)
Jiang, M.: Inapproximability of maximal strip recovery. In: Dong, Y., Du, D.-Z., Ibarra, O. (eds.) ISAAC 2009. LNCS, vol. 5878, pp. 616–625. Springer, Heidelberg (2009)
Jiang, M.: Inapproximability of maximal strip recovery, II. In: Proceedings of the 4th Annual Frontiers of Algorithmics Workshop, FAW 2010 (to appear 2010)
Vazirani, V.: Approximation Algorithms. Springer, Heidelberg (2001)
Wang, L., Zhu, B.: On the tractability of maximal strip recovery. J. of Computational Biology (to appear 2010); An earlier version appeared in TAMC 2009
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
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Zhu, B. (2010). Efficient Exact and Approximate Algorithms for the Complement of Maximal Strip Recovery. In: Chen, B. (eds) Algorithmic Aspects in Information and Management. AAIM 2010. Lecture Notes in Computer Science, vol 6124. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14355-7_33
Download citation
DOI: https://doi.org/10.1007/978-3-642-14355-7_33
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-14354-0
Online ISBN: 978-3-642-14355-7
eBook Packages: Computer ScienceComputer Science (R0)