STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Transforming cabbage into turnip: polynomial algorithm for sorting signed permutations by reversals
Journal of the ACM (JACM)
Genomic distances under deletions and insertions
Theoretical Computer Science - Special papers from: COCOON 2003
Mathematics of Evolution and Phylogeny
Mathematics of Evolution and Phylogeny
On the similarity of sets of permutations and its applications to genome comparison
COCOON'03 Proceedings of the 9th annual international conference on Computing and combinatorics
The approximability of the exemplar breakpoint distance problem
AAIM'06 Proceedings of the Second international conference on Algorithmic Aspects in Information and Management
Conserved interval distance computation between non-trivial genomes
COCOON'05 Proceedings of the 11th annual international conference on Computing and Combinatorics
RNA multiple structural alignment with longest common subsequences
COCOON'05 Proceedings of the 11th annual international conference on Computing and Combinatorics
Comparing Genomes with Duplications: A Computational Complexity Point of View
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
Approximability and Fixed-Parameter Tractability for the Exemplar Genomic Distance Problems
TAMC '09 Proceedings of the 6th Annual Conference on Theory and Applications of Models of Computation
The zero exemplar distance problem
RECOMB-CG'10 Proceedings of the 2010 international conference on Comparative genomics
Non-breaking similarity of genomes with gene repetitions
CPM'07 Proceedings of the 18th annual conference on Combinatorial Pattern Matching
An Exact Algorithm for the Zero Exemplar Breakpoint Distance Problem
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
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In this paper we present several lower bounds on the approximation of the exemplar conserved interval distance problem of genomes. We first prove that the exemplar conserved interval distance problem cannot be approximated within a factor of clogn for some constant c0 in polynomial time, unless P=NP. We then prove that it is NP-complete to decide whether the exemplar conserved interval distance between any two sets of genomes is zero or not. This result implies that the exemplar conserved interval distance problem does not admit any approximation in polynomial time, unless P=NP. In fact, this result holds even when a gene appears in each of the given genomes at most three times. Finally, we strengthen the second result under a weaker definition of approximation (which we call weak approximation). We show that the exemplar conserved interval distance problem does not admit a weak approximation within a factor of m, where m is the maximum length of the given genomes.