Abstract
In this paper we define a new similarity measure, the non-breaking similarity, which is the complement of the famous breakpoint distance between genomes (in general, between any two sequences drawn from the same alphabet). When the two input genomes \({\cal G}\) and \({\cal H}\), drawn from the same set of n gene families, contain gene repetitions, we consider the corresponding Exemplar Non-breaking Similarity problem (ENbS) in which we need to delete repeated genes in \({\cal G}\) and \({\cal H}\) such that the resulting genomes G and H have the maximum non-breaking similarity. We have the following results.
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For the Exemplar Non-breaking Similarity problem, we prove that the Independent Set problem can be linearly reduced to this problem. Hence, ENbS does not admit any factor-n 1 − ε polynomial-time approximation unless P=NP. (Also, ENbS is W[1]-complete.)
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We show that for several practically interesting cases of the Exemplar Non-breaking Similarity problem, there are polynomial time algorithms.
This research is supported by Louisiana Board of Regents under contract number LEQSF(2004-07)-RD-A-35, NSF grant CCF-0546509, NSERC grant 261290-03 and Montana EPSCOR’s Visiting Scholar’s Program.
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Chen, Z., Fu, B., Xu, J., Yang, B., Zhao, Z., Zhu, B. (2007). Non-breaking Similarity of Genomes with Gene Repetitions. In: Ma, B., Zhang, K. (eds) Combinatorial Pattern Matching. CPM 2007. Lecture Notes in Computer Science, vol 4580. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73437-6_14
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DOI: https://doi.org/10.1007/978-3-540-73437-6_14
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