Abstract
In this paper we present the first set of approximation and inapproximability results for the Exemplar Breakpoint Distance Problem. Our inapproximability results hold for the simplest case between only two genomes \({\cal G}\) and \({\cal H}\), each containing only one sequence of genes (possibly with repetitions).
– For the general Exemplar Breakpoint Distance Problem, we prove that the problem does not admit any approximation unless P=NP; in fact, this result holds even when a gene appears in \({\cal G}\) (\({\cal H}\)) at most three times.
– Even on a weaker definition of approximation (which we call weak approximation), we show that the problem does not admit a weak approximation with a factor m 1 − − ε, where m is the maximum length of \({\cal G}\) and \({\cal H}\).
– We present a factor-2(1 + logn) approximation for an interesting special case, namely, one of the two genomes is a k-span genome (i.e., all genes in the same gene family are within a distance k = O(logn)), where n is the number of gene families in \({\cal G}\) and \({\cal H}\).
This research is supported by Louisiana Board of Regents under contract number LEQSF(2004-07)-RD-A-35 and MSU-Bozeman’s Short-term Professional Development Leave Program.
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Chen, Z., Fu, B., Zhu, B. (2006). The Approximability of the Exemplar Breakpoint Distance Problem. In: Cheng, SW., Poon, C.K. (eds) Algorithmic Aspects in Information and Management. AAIM 2006. Lecture Notes in Computer Science, vol 4041. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11775096_27
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