Transforming cabbage into turnip: polynomial algorithm for sorting signed permutations by reversals
Journal of the ACM (JACM)
Some APX-completeness results for cubic graphs
Theoretical Computer Science
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
On Some Tighter Inapproximability Results (Extended Abstract)
ICAL '99 Proceedings of the 26th International Colloquium on Automata, Languages and Programming
Exemplar Longest Common Subsequence
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
Comparing Genomes with Duplications: A Computational Complexity Point of View
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
Vertex cover might be hard to approximate to within 2-ε
Journal of Computer and System Sciences
The ExemplarBreakpointDistance for Non-trivial Genomes Cannot Be Approximated
WALCOM '09 Proceedings of the 3rd International Workshop on Algorithms and Computation
Power boosts for cluster tests
RCG'05 Proceedings of the 2005 international conference on Comparative Genomics
The approximability of the exemplar breakpoint distance problem
AAIM'06 Proceedings of the Second international conference on Algorithmic Aspects in Information and Management
On sorting unsigned permutations by double-cut-and-joins
Journal of Combinatorial Optimization
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Given two genomes possibly with duplicate genes, the exemplar distance problem is that of removing all but one copy of each gene in each genome, so as to minimize the distance between the two reduced genomes according to some measure. Let $((s,t))$-exemplar distance denote the exemplar distance problem on two genomes $(G_1)$ and $(G_2)$, where each gene occurs at most $(s)$ times in $(G_1)$ and at most $(t)$ times in $(G_2)$. We show that the simplest nontrivial variant of the exemplar distance problem, $((1,2))$-Exemplar Distance, is already hard to approximate for a wide variety of distance measures, including both popular genome rearrangement measures such as adjacency disruptions, signed reversals, and signed double-cut-and-joins, and classic string edit distance measures such as Levenshtein and Hamming distances.