The Problem of Chromosome Reincorporation in DCJ Sorting and Halving

@inproceedings{Kovc2010ThePO,
  title={The Problem of Chromosome Reincorporation in DCJ Sorting and Halving},
  author={Jakub Kov{\'a}c and Mar{\'i}lia Dias Vieira Braga and Jens Stoye},
  booktitle={RECOMB-CG},
  year={2010}
}
We study two problems in the double cut and join (DCJ) model: sorting - transforming one multilinear genome into another and halving - transforming a duplicated genome into a perfectly duplicated one. The DCJ model includes rearrangement operations such as reversals, translocations, fusions and fissions. We can also mimic transpositions or block interchanges by two operations: we extract an appropriate segment of a chromosome, creating a temporary circular chromosome, and in the next step we… 

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References

SHOWING 1-10 OF 17 REFERENCES

Computation of Perfect DCJ Rearrangement Scenarios with Linear and Circular Chromosomes

TLDR
It is shown that computing the minimum perfect DCJ rearrangement scenario is NP-hard, and an exact algorithm which exponential running time is bounded in terms of a specific pattern used in the NP-completeness proof is described.

Advances on sorting by reversals

Efficient sorting of genomic permutations by translocation, inversion and block interchange

TLDR
A universal double-cut-and-join operation that accounts for inversions, translocations, fissions and fusions, but also produces circular intermediates which can be reabsorbed, which converts one multi-linear chromosome genome to another in the minimum distance.

Sorting signed permutations by inversions in O(nlogn) time.

TLDR
Two new sorting algorithms are provided, a simple and fast randomized algorithm and a deterministic refinement, which conclude (but do not prove) that almost all signed permutations can be sorted by inversions in O(nlogn) time.

Genome Halving under DCJ Revisited

TLDR
The Genome Halving Problem for the DCJ distance is revisited and a genome model such that constraints for linear genomes, as well as the ones for circular genomes are taken into account is proposed.

A Unifying View of Genome Rearrangements

TLDR
A simple way to apply the double cut and join operation to the most general type of genomes with a mixed collection of linear and circular chromosomes is shown and a graph structure is described that allows simplifying the theory and distance computation considerably, as neither capping nor concatenation of the linear chromosomes are necessary.

Multichromosomal median and halving problems under different genomic distances

TLDR
This theoretical study clears up a wide swathe of the algorithmical study of genome rearrangements with multiple multichromosomal genomes by settling the complexity of several genome median and halving problems, including a surprising polynomial result for the breakpoint median and guided halvingblems in genomes with circular and linear chromosomes.

Sorting Permutations by Block-Interchanges

The Reconstruction of Doubled Genomes

TLDR
This work presents exact algorithms for reconstructing the ancestral doubled genome in linear time, minimizing the number of rearrangement mutations required to derive the observed order of genes along the present-day chromosomes.

Sorting signed permutations by reversals, revisited