Abstract
The Radiation Hybrid Map Construction problem (RHMC) is of prime interest in the area of Bioinformatics, and is concerned with reconstructing a genome from a set of given gene clusters. The problem is \(\mbox{$\mathcal{NP}$}\)-complete, even for the special case when the cardinality of each cluster is 2. Recently, Zhang et al. considered the case when the cardinality of each cluster is at most three, and proved that RHMC in this case is fixed-parameter tractable. They asked whether RHMC is fixed-parameter tractable for any fixed upper bound on the cluster cardinality.
In this paper, we answer the question of Zhang et al. in the affirmative by showing that RHMC is fixed-parameter tractable when the cardinality of each cluster is at most d, for any nonnegative integer-constant d.
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References
Bodlaender, H.: A Linear-Time Algorithm for Finding Tree-Decompositions of Small Treewidth. SIAM Journal on Computing 25(6), 1305–1317 (1996)
Bodlaender, H., Fellows, M., Hallett, M., Wareham, H.: Parameterized complexity analysis in computational biology. Computer Applications in the Biosciences 11, 49–57 (1995)
Bodlaender, H., Fellows, M., Hallett, M., Wareham, H.: The parameterized complexity of the longest common subsequence problem. Theoretical Computer Science 147, 31–54 (1995)
Bodlaender, H.L., Thilikos, D.M.: Computing Small Search Numbers in Linear Time. In: Downey, R.G., Fellows, M.R., Dehne, F. (eds.) IWPEC 2004. LNCS, vol. 3162, pp. 37–48. Springer, Heidelberg (2004)
Cesati, M., Wareham, H.: Parameterized complexity analysis in robot motion planning. In: Proceedings of the 25th IEEE International Conference on Systems, Man and Cybernetics, pp. 880–885 (1995)
Chen, Z.-Z., Lin, G., Wang, L.: An approximation algorithm for the minimum co-path set problem. Algorithmica 60(4), 969–986 (2011)
Cheng, Y., Cai, Z., Goebel, R., Lin, G., Zhu, B.: The radiation hybrid map construction problem: recognition, hardness, and approximation algorithms (2008) (unpublished manuscript)
Cox, D., Burmeister, M., Price, E., Kim, S., Myers, R.: Radiation hybrid mapping: a somatic cell genetic method for constructing high resolution maps of mammalian chromosomes. Science 250, 245–250 (1990)
De Givry, S., Bouchez, M., Chabrier, P., Milan, D., Schiex, T.: Carh ta Gene: multipopulation integrated genetic and radiation hybrid mapping. Bioinformatics 21(8), 1703 (2005)
Downey, R., Evans, P., Fellows, M.: Parameterized learning complexity. In: Proceedings of the 6th ACM Workshop on Computational Learning Theory, pp. 51–57 (1993)
Downey, R., Fellows, M.: Parameterized complexity. Springer, New York (1999)
Downey, R., Fellows, M., Stege, U.: Parameterized complexity: a framework for systematically confronting computational intractability. In: Roberts, F., Kratochvil, J., Nešetřil, J. (eds.) Contemporary Trends in Discrete Mathematics, AMS-DIMACS Proceedings, pp. 49–99. American Mathematical Society (1999)
Faraut, T., De Givry, S., Chabrier, P., Derrien, T., Galibert, F., Hitte, C., Schiex, T.: A comparative genome approach to marker ordering. Bioinformatics 23(2), e50 (2007)
Fellows, M., Hallett, M., Wareham, H.: DNA physical mapping: three ways of difficult. In: Lengauer, T. (ed.) ESA 1993. LNCS, vol. 726, pp. 157–168. Springer, Heidelberg (1993)
Fellows, M., Hallett, M., Wareham, H.: Fixed-parameter complexity and cryptography. In: Moreno, O., Cohen, G., Mora, T. (eds.) AAECC 1993. LNCS, vol. 673, pp. 121–131. Springer, Heidelberg (1993)
Fellows, M., Langston, M.: On search, decision and the efficiency of polynomial-time algorithms. In: Proceedings of the 21st ACM Symposium on Theory of Computing (STOC), pp. 501–512 (1989)
Fishburn, P.: Interval orders and interval graphs: A study of partially ordered sets. Wiley-Interscience Series in Discrete Mathematics, New York (1985)
Flum, J., Grohe, M.: Parameterized complexity theory. Springer-Verlag New York Inc. (2006)
Jiang, H., Zhu, B.: Weak Kernels. Electronic Colloquium on Computational Complexity (ECCC)Â 17, 5 (2010)
Kaplan, H., Shamir, R., Tarjan, R.: Tractability of parameterized completion problems on chordal, strongly chordal, and proper interval graphs. SIAM Journal on Computing 28, 880–892 (1999)
Niedermeier, R.: Invitation to fixed-parameter algorithms. Oxford University Press, USA (2006)
Rafiey, A.: Single Exponential FPT Algorithm for Interval Vertex Deletion and Interval Completion Problem, http://arxiv.org/pdf/1211.4629v1.pdf
Richard, C., Withers, D., Meeker, T., Maurer, S., Evans, G., Myers, R., Cox, D.: A radiation hybrid map of the proximal long arm of human chromosome 11 containing the multiple endocrine neoplasia type 1 (MEN-1) and bcl-1 disease loci. American Journal of Human Genetics 49(6), 1189 (1991)
Slonim, D., Kruglyak, L., Stein, L., Lander, E.: Building human genome maps with radiation hybrids. Journal of Computational Biology 4(4), 487–504 (1997)
Zhang, C., Jiang, H., Zhu, B.: Radiation hybrid map construction problem parameterized. In: Lin, G. (ed.) COCOA 2012. LNCS, vol. 7402, pp. 127–137. Springer, Heidelberg (2012)
West, D.: Introduction to graph theory. Prentice Hall Inc., Upper Saddle River (2006)
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Kanj, I., Xia, G., Zhu, B. (2013). The Radiation Hybrid Map Construction Problem Is FPT. In: Cai, Z., Eulenstein, O., Janies, D., Schwartz, D. (eds) Bioinformatics Research and Applications. ISBRA 2013. Lecture Notes in Computer Science(), vol 7875. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38036-5_5
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DOI: https://doi.org/10.1007/978-3-642-38036-5_5
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