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Multichromosomal median and halving problems under different genomic distances.

Tannier E, Zheng C, Sankoff D - BMC Bioinformatics (2009)

Bottom Line: Although the multichromosomal case has often been assumed to be a simple generalization of the unichromosomal case, it is also a relaxation so that complexity in this context does not follow from existing results, and is open for all distances.We list the remaining open problems.This theoretical study clears up a wide swathe of the algorithmical study of genome rearrangements with multiple multichromosomal genomes.

View Article: PubMed Central - HTML - PubMed

Affiliation: INRIA Rhône-Alpes, Inovallée, Montbonnot, Saint Ismier Cedex, France. Eric.Tannier@inria.fr

ABSTRACT

Background: Genome median and genome halving are combinatorial optimization problems that aim at reconstructing ancestral genomes as well as the evolutionary events leading from the ancestor to extant species. Exploring complexity issues is a first step towards devising efficient algorithms. The complexity of the median problem for unichromosomal genomes (permutations) has been settled for both the breakpoint distance and the reversal distance. Although the multichromosomal case has often been assumed to be a simple generalization of the unichromosomal case, it is also a relaxation so that complexity in this context does not follow from existing results, and is open for all distances.

Results: We settle here the complexity of several genome median and halving problems, including a surprising polynomial result for the breakpoint median and guided halving problems in genomes with circular and linear chromosomes, showing that the multichromosomal problem is actually easier than the unichromosomal problem. Still other variants of these problems are NP-complete, including the DCJ double distance problem, previously mentioned as an open question. We list the remaining open problems.

Conclusion: This theoretical study clears up a wide swathe of the algorithmical study of genome rearrangements with multiple multichromosomal genomes.

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Related in: MedlinePlus

Reduction of BGD to DCJ guided halving problem. The left hand graph is the balanced bicoloured graph G, and the right hand graph represents the adjacencies of the genomes Δ and Π. Adjacencies of Π are doubled in the drawing to be presented with the doubled genes.
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Figure 8: Reduction of BGD to DCJ guided halving problem. The left hand graph is the balanced bicoloured graph G, and the right hand graph represents the adjacencies of the genomes Δ and Π. Adjacencies of Π are doubled in the drawing to be presented with the doubled genes.

Mentions: Let G be a balanced bicoloured graph on n vertices. Define the gene set as a set containing one gene X for every degree 2 vertex of G, and two genes X and Y for every degree 4 vertex of G. From G, we define one genome Π and one all-duplicates genome Δ on as illustrated in Figure 8.


Multichromosomal median and halving problems under different genomic distances.

Tannier E, Zheng C, Sankoff D - BMC Bioinformatics (2009)

Reduction of BGD to DCJ guided halving problem. The left hand graph is the balanced bicoloured graph G, and the right hand graph represents the adjacencies of the genomes Δ and Π. Adjacencies of Π are doubled in the drawing to be presented with the doubled genes.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC2683817&req=5

Figure 8: Reduction of BGD to DCJ guided halving problem. The left hand graph is the balanced bicoloured graph G, and the right hand graph represents the adjacencies of the genomes Δ and Π. Adjacencies of Π are doubled in the drawing to be presented with the doubled genes.
Mentions: Let G be a balanced bicoloured graph on n vertices. Define the gene set as a set containing one gene X for every degree 2 vertex of G, and two genes X and Y for every degree 4 vertex of G. From G, we define one genome Π and one all-duplicates genome Δ on as illustrated in Figure 8.

Bottom Line: Although the multichromosomal case has often been assumed to be a simple generalization of the unichromosomal case, it is also a relaxation so that complexity in this context does not follow from existing results, and is open for all distances.We list the remaining open problems.This theoretical study clears up a wide swathe of the algorithmical study of genome rearrangements with multiple multichromosomal genomes.

View Article: PubMed Central - HTML - PubMed

Affiliation: INRIA Rhône-Alpes, Inovallée, Montbonnot, Saint Ismier Cedex, France. Eric.Tannier@inria.fr

ABSTRACT

Background: Genome median and genome halving are combinatorial optimization problems that aim at reconstructing ancestral genomes as well as the evolutionary events leading from the ancestor to extant species. Exploring complexity issues is a first step towards devising efficient algorithms. The complexity of the median problem for unichromosomal genomes (permutations) has been settled for both the breakpoint distance and the reversal distance. Although the multichromosomal case has often been assumed to be a simple generalization of the unichromosomal case, it is also a relaxation so that complexity in this context does not follow from existing results, and is open for all distances.

Results: We settle here the complexity of several genome median and halving problems, including a surprising polynomial result for the breakpoint median and guided halving problems in genomes with circular and linear chromosomes, showing that the multichromosomal problem is actually easier than the unichromosomal problem. Still other variants of these problems are NP-complete, including the DCJ double distance problem, previously mentioned as an open question. We list the remaining open problems.

Conclusion: This theoretical study clears up a wide swathe of the algorithmical study of genome rearrangements with multiple multichromosomal genomes.

Show MeSH
Related in: MedlinePlus