Abstract
Given a set of n taxa S, exactly one topology for every subset of four taxa, and a positive integer k as the parameter, the parameterized Minimum Quartet Inconsistency (MQI) problem is to decide whether we can find an evolutionary tree inducing a set of quartet topologies that differs from the given set in at most k quartet topologies. The best fixed-parameter algorithm devised so far for the parameterized MQI problem runs in time O(4k n + n 4). In this paper, first we present an O(3.0446k n + n 4) algorithm and an O(2.0162k n 3 + n 5) algorithm. Finally, we give an O *((1 + ε)k) algorithm with an arbitrarily small constant ε> 0.
This research was supported by NSC-DAAD Sandwich Program and partially supported by the National Science Council of Taiwan under grant no. NSC 96-2221-E-194-045-MY3, and was carried out at RWTH Aachen University, Germany.
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
Ben-Dor, A., Chor, B., Graur, D., Ophir, R., Pelleg, D.: From four-taxon trees to phylogenies: The case of mammalian evolution. In: Proceedings of the RECOMB, pp. 9–19 (1998)
Bandelt, H.J., Dress, A.: Reconstructing the shape of a tree from observed dissimilarity date. Adv. Appl. Math. 7, 309–343 (1986)
Berry, V., Jiang, T., Kearney, P.E., Li, M., Wareham, H.T.: Quartet cleaning: Improved algorithms and simulations. In: Nešetřil, J. (ed.) ESA 1999. LNCS, vol. 1643, pp. 313–324. Springer, Heidelberg (1999)
Cho, B.: From quartets to phylogenetic trees. In: Rovan, B. (ed.) SOFSEM 1998. LNCS, vol. 1521, pp. 36–53. Springer, Heidelberg (1998)
Downey, R.G., Fellows, M.R.: Parameterized Complexity. Springer, Heidelberg (1999)
Erdős, P., Steel, M., Székely, L., Warnow, T.: A few logs suffice to build (almost) all trees (Part 1). Random Struct. Alg. 14, 153–184 (1999)
Greene, D.H., Knuth, D.E.: Mathematics for the Analysis of Algorithms, 2nd edn. Progress in Computer Science. Birkhauser, Boston (1982)
Gramm, J., Niedermeier, R.: A fixed-parameter algorithm for minimum quartet inconsistency. J. Comput. System Sci. 67, 723–741 (2003)
Jiang, T., Kearney, P.E., Li, M.: Some open problems in computational molecular biology. J. Algorithms 34, 194–201 (2000)
Jiang, T., Kearney, P.E., Li, M.: A polynomial time approximation scheme for inferring evolutionary tree from quartet topologies and its application. SIAM J. Comput. 30, 1942–1961 (2001)
Steel, M.: The complexity of reconstructing trees from qualitative characters and subtrees. J. Classification 9, 91–116 (1992)
Niedermeier, R.: Invitation to Fixed-Parameter Algorithms. Oxford University Press, Oxford (2006)
Niedermeier, R., Rossmanith, P.: A general method to speed up fixed-parameter algorithms. Inform. Process. Lett. 73, 125–129 (2000)
Wu, G., You, J.-H., Lin, G.: A lookahead branch-and-bound algorithm for the maximum quartet consistency problem. In: Casadio, R., Myers, G. (eds.) WABI 2005. LNCS (LNBI), vol. 3692, pp. 65–76. Springer, Heidelberg (2005)
Wu, G., You, J.-H., Lin, G.: A polynomial time algorithm for the minimum quartet inconsistency problem with O(n) quartet errors. Inform. Process. Lett. 100, 167–171 (2006)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Chang, MS., Lin, CC., Rossmanith, P. (2008). New Fixed-Parameter Algorithms for the Minimum Quartet Inconsistency Problem. In: Grohe, M., Niedermeier, R. (eds) Parameterized and Exact Computation. IWPEC 2008. Lecture Notes in Computer Science, vol 5018. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-79723-4_8
Download citation
DOI: https://doi.org/10.1007/978-3-540-79723-4_8
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-79722-7
Online ISBN: 978-3-540-79723-4
eBook Packages: Computer ScienceComputer Science (R0)