# A Path-Deformation Framework for Determining Weighted Genome Rearrangement Distance

@article{Bhatia2020APF, title={A Path-Deformation Framework for Determining Weighted Genome Rearrangement Distance}, author={Sangeeta Bhatia and Attila Egri-Nagy and Stuart Serdoz and Cheryl E. Praeger and Volker Gebhardt and Andrew R. Francis}, journal={Frontiers in Genetics}, year={2020}, volume={11} }

Measuring the distance between two bacterial genomes under the inversion process is usually done by assuming all inversions to occur with equal probability. Recently, an approach to calculating inversion distance using group theory was introduced, and is effective for the model in which only very short inversions occur. In this paper, we show how to use the group-theoretic framework to establish minimal distance for any weighting on the set of inversions, generalizing previous approaches. To do…

## One Citation

A mean first passage time genome rearrangement distance

- MathematicsJournal of mathematical biology
- 2020

A new way to define a genome rearrangement distance is introduced, using the concept of mean first passage time from probability theory, which provides a genuine metric on genome space.

## References

SHOWING 1-10 OF 53 REFERENCES

Group-theoretic models of the inversion process in bacterial genomes

- Mathematics, BiologyJournal of mathematical biology
- 2014

A group-theoretic framework is suggested that by lifting the problem from circular permutations to the affine symmetric group, the inversion distance can be found in polynomial time for a model in which inversions are restricted to acting on two regions.

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.

Sorting by Transpositions

- BiologySIAM J. Discret. Math.
- 1998

The paper addresses the problem of genome comparison versus classical gene comparison and presents algorithms to analyze rearrangements in genomes evolving by transpositions and derive lower bounds on {\em transposition distance} between permutations and present approximation algorithms for sorting byTranspositions.

On the tandem duplication-random loss model of genome rearrangement

- BiologySODA '06
- 2006

A notion of distance between two genomes is formalized and it is shown how to compute it efficiently for two interesting regions of the parameter space and an O(log log n) additive approximation algorithm is given for the latter.

Sorting permutations by tanspositions

- BiologySODA '95
- 1995

The paper addresses the problem of genome comparison versus classical gene comparison and presents algorithms to analyze rearrangements in genomes evolving by transpositions and derive lower bounds on tmnsposition distance between permutations and present approximation algorithms for sorting by transposition.

An Exact Algorithm to Compute the DCJ Distance for Genomes with Duplicate Genes

- Biology, Computer ScienceRECOMB
- 2014

This paper proposes an ILPi¾źinteger linear programming formulation to compute the DCJ distance between two genomes with duplicate genes and provides an efficient preprocessing approach to simplify the ILP formulation while preserving optimality.

Genomic sorting with length-weighted reversals.

- Computer ScienceGenome informatics. International Conference on Genome Informatics
- 2002

This work introduces a new cost model in which the lengths of the reversed sequences play a role, allowing more flexibility in accounting for mutation phenomena, and proposes an efficient, novel algorithm that takes length into account as an optimization criterion.

Sorting signed permutations by short operations

- MathematicsAlgorithms for Molecular Biology
- 2015

The problem of sorting a signed permutation by short operations is investigated and the approximation ratios of the approximation algorithms cannot be smaller than 3, which means that the approximation ratio of the 3-approximation algorithm is tight.

An algebraic view of bacterial genome evolution

- MathematicsJournal of mathematical biology
- 2014

A family of biological problems in bacterial genome evolution for which an algebraic viewpoint may capture a deeper structure behind biological phenomena is discussed, and the prospect that the tools developed by algebraists over the last century might provide insight to this area of evolutionary biology is raised.