# The Genesis of the DCJ Formula

@inproceedings{Bergeron2013TheGO, title={The Genesis of the DCJ Formula}, author={Anne Bergeron and Jens Stoye}, booktitle={Models and Algorithms for Genome Evolution}, year={2013} }

The formula N−(C+I/2) to compute the number of Double-Cut-and-Join operations needed to transform one genome into another is both simple and easy to prove. When it was published, in 2006, we omitted all details on how it was constructed. In this chapter, we will give an elementary treatment on the intuitions and methods underlying the formula, showing that simplicity is sometimes difficult to achieve. We will also prove that this formula is one among an infinite number of candidates, and that…

## 2 Citations

### Genome Rearrangement Analysis: Cut and Join Genome Rearrangements and Gene Cluster Preserving Approaches.

- BiologyMethods in molecular biology
- 2018

In this chapter, the border between algorithmically "easy" and "hard" rearrangement problems is sketched and a brief review is given on the available software tools for genome rearrangements analysis.

### Comparative Genomics

- BiologyMethods in Molecular Biology
- 2018

This chapter covers the theory and practice of ortholog gene set computation, and provides an overview of practical considerations intended for researchers who need to determine orthologous genes from a collection of annotated genomes.

## References

SHOWING 1-10 OF 10 REFERENCES

### Rearrangement Models and Single-Cut Operations

- MathematicsRECOMB-CG
- 2009

A formal set-theoretic definition of a model is given, which allows to investigate and prove relationships between distances under various existing and new models, and initiate the formal study of single-cut operations by giving a linear time algorithm for the distance problem under a new single- cut and join model.

### SCJ: A Breakpoint-Like Distance that Simplifies Several Rearrangement Problems

- Computer ScienceIEEE/ACM Transactions on Computational Biology and Bioinformatics
- 2011

This paper calls it SCJ for single-cut-or-join, in analogy to the popular double cut and join (DCJ) measure, and shows that several genome rearrangement problems become easy for SCJ, and provides linear and higher polynomial time algorithms for them.

### Extending the Algebraic Formalism for Genome Rearrangements to Include Linear Chromosomes

- Computer ScienceIEEE/ACM Transactions on Computational Biology and Bioinformatics
- 2013

The adjacency algebraic theory is introduced, extending the original mathematics to linear chromosomes in a very natural way, and allowing the original algebraic distance formula to be used to the general multichromosomal case, with both linear and circular chromosomes.

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

- BiologyBioinform.
- 2005

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.

### Transforming men into mice (polynomial algorithm for genomic distance problem)

- BiologyProceedings of IEEE 36th Annual Foundations of Computer Science
- 1995

A duality theorem is proved which expresses the genomic distance in terms of easily computable parameters reflecting different combinatorial properties of sets of strings and leads to a polynomial time algorithm for computing most parsimonious rearrangement scenarios for human-mouse evolution.

### AN ALTERNATIVE ALGEBRAIC FORMALISM FOR GENOME REARRANGEMENTS

- Mathematics
- 2000

The recent theory of genome rearrangements is related to the theory of permutation groups in a new way and this work intends to give the area a strong algebraic formalism, much as analytic geometry provided an alternative geometric arguments based on pictures.

### Multichromosomal median and halving problems under different genomic distances

- BiologyBMC Bioinformatics
- 2008

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.

### Inversions in the Chromosomes of Drosophila Pseudoobscura.

- BiologyGenetics
- 1938

Comparisons of the different gene arrangements in the chromosomes of strains of D. pseudoobscura coming from different geographical regions may throw light on the historical relationships of these structures, and consequently on the history of the species as a whole.

### Comparative Genomics: "Empirical And Analytical Approaches To Gene Order Dynamics, Map Alignment And The Evolution Of Gene Families"

- Biology
- 2000

A comparison of Gene and Genome Duplication and Multi-gene Families and Combinatorial Algorithms: A New Set of Problems for a New Kind of Data.

### A Unifying View of Genome Rearrangements

- Computer ScienceWABI
- 2006

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.