On the approximability of the exemplar adjacency number problem for genomes with gene repetitions

Zhixiang Chen, Bin Fu, Randy Goebel, Guohui Lin, Weitian Tong, Jinhui Xu, Boting Yang, Zhiyu Zhao, Binhai Zhu

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


In this paper, we apply a measure, exemplar adjacency number, which complements and extends the well-studied breakpoint distance between two permutations, to measure the similarity between two genomes (or in general, between any two sequences drawn from the same alphabet). For two genomes G and H drawn from the same set of n gene families and containing gene repetitions, we consider the corresponding Exemplar Adjacency Number problem (EAN), in which we delete duplicated genes from G and H such that the resultant exemplar genomes (permutations) G and H have the maximum adjacency number. We obtain the following results. First, we prove that the one-sided 2-repetitive EAN problem, i.e., when one of G and H is given exemplar and each gene occurs in the other genome at most twice, can be linearly reduced from the Maximum Independent Set problem. This implies that EAN does not admit any O(n0.5-ε)-approximation algorithm, for any ε>0, unless P = NP. This hardness result also implies that EAN, parameterized by the optimal solution value, is W[1]-hard. Secondly, we show that the two-sided 2-repetitive EAN problem has an O(n0.5)-approximation algorithm, which is tight up to a constant factor.

Original languageEnglish (US)
Pages (from-to)59-65
Number of pages7
JournalTheoretical Computer Science
Issue numberC
StatePublished - 2014


  • Adjacency
  • Approximation algorithm
  • Breakpoint
  • Genome comparison
  • NP-hard

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)


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