The approximability of the exemplar breakpoint distance problem

  • Authors:

  • Zhixiang Chen;Bin Fu;Binhai Zhu

  • Affiliations:

  • Department of Computer Science, University of Texas-Pan American, Edinburg, TX;Department of Computer Science, Research Institute for Children, University of New Orleans, New Orleans, LA;Department of Computer Science, Montana State University, Bozeman, MT

  • Venue:
  • AAIM'06 Proceedings of the Second international conference on Algorithmic Aspects in Information and Management
  • Year:
  • 2006

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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 m1−−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 ${\cal H}$.