A threshold of ln n for approximating set cover
Journal of the ACM (JACM)
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Genomic distances under deletions and insertions
Theoretical Computer Science - Special papers from: COCOON 2003
Assignment of Orthologous Genes via Genome Rearrangement
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
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
Maximizing synteny blocks to identify ancestral homologs
RCG'05 Proceedings of the 2005 international conference on Comparative Genomics
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
Conserved interval distance computation between non-trivial genomes
COCOON'05 Proceedings of the 11th annual international conference on Computing and Combinatorics
Lower bounds on the approximation of the exemplar conserved interval distance problem of genomes
COCOON'06 Proceedings of the 12th annual international conference on Computing and Combinatorics
Inferring positional homologs with common intervals of sequences
RCG'06 Proceedings of the RECOMB 2006 international conference on Comparative Genomics
How pseudo-boolean programming can help genome rearrangement distance computation
RCG'06 Proceedings of the RECOMB 2006 international conference on Comparative Genomics
A parsimony approach to genome-wide ortholog assignment
RECOMB'06 Proceedings of the 10th annual international conference on Research in Computational Molecular Biology
The ExemplarBreakpointDistance for Non-trivial Genomes Cannot Be Approximated
WALCOM '09 Proceedings of the 3rd International Workshop on Algorithms and Computation
Comparing Bacterial Genomes by Searching Their Common Intervals
BICoB '09 Proceedings of the 1st International Conference on Bioinformatics and Computational Biology
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
Finding Nested Common Intervals Efficiently
RECOMB-CG '09 Proceedings of the International Workshop on Comparative Genomics
RECOMB-CG '09 Proceedings of the International Workshop on Comparative Genomics
Inferring a duplication, speciation and loss history from a gene tree
RECOMB-CG'07 Proceedings of the 2007 international conference on Comparative genomics
A polynomial algebra method for computing exemplar breakpoint distance
ISBRA'11 Proceedings of the 7th international conference on Bioinformatics research and applications
An algorithmic view on multi-related-segments: a unifying model for approximate common interval
TAMC'12 Proceedings of the 9th Annual international conference on Theory and Applications of Models of Computation
Inapproximability of (1,2)-exemplar distance
ISBRA'12 Proceedings of the 8th international conference on Bioinformatics Research and Applications
Inapproximability of (1,2)-Exemplar Distance
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
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 are interested in the computational complexity of computing (dis)similarity measures between two genomes when they contain duplicated genes or genomic markers, a problem that happens frequently when comparing whole nuclear genomes. Recently, several methods ( [1], [2]) have been proposed that are based on two steps to compute a given (dis)similarity measure M between two genomes G_1 and G_2: first, one establishes a oneto- one correspondence between genes of G_1 and genes of G_2 ; second, once this correspondence is established, it defines explicitly a permutation and it is then possible to quantify their similarity using classical measures defined for permutations, like the number of breakpoints. Hence these methods rely on two elements: a way to establish a one-to-one correspondence between genes of a pair of genomes, and a (dis)similarity measure for permutations. The problem is then, given a (dis)similarity measure for permutations, to compute a correspondence that defines an optimal permutation for this measure. We are interested here in two models to compute a one-to-one correspondence: the exemplar model, where all but one copy are deleted in both genomes for each gene family, and the matching model, that computes a maximal correspondence for each gene family. We show that for these two models, and for three (dis)similarity measures on permutations, namely the number of common intervals, the maximum adjacency disruption (MAD) number and the summed adjacency disruption (SAD) number, the problem of computing an optimal correspondence is NP-complete, and even APXhard for the MAD number and SAD number.