### Abstract

The Single Cut or Join (SCJ) operation on genomes, generalizing chromosome evolution by fusions and fissions, is the computationally simplest known model of genome rearrangement. While most genome rearrangement problems are already hard when comparing three genomes, it is possible to compute in polynomial time a most parsimonious SCJ scenario for an arbitrary number of genomes related by a binary phylogenetic tree.Here we consider the problems of sampling and counting the most parsimonious SCJ scenarios. We show that both the sampling and counting problems are easy for two genomes, and we relate SCJ scenarios to alternating permutations. However, for an arbitrary number of genomes related by a binary phylogenetic tree, the counting and sampling problems become hard. We prove that if a Fully Polynomial Randomized Approximation Scheme or a Fully Polynomial Almost Uniform Sampler exist for the most parsimonious SCJ scenario, then RP = NP.The proof has a wider scope than genome rearrangements: the same result holds for parsimonious evolutionary scenarios on any set of discrete characters.

Original language | English |
---|---|

Pages (from-to) | 83-98 |

Number of pages | 16 |

Journal | Theoretical Computer Science |

Volume | 552 |

Issue number | C |

DOIs | |

Publication status | Published - 2014 |

### Fingerprint

### Keywords

- Computations on discrete structures
- Counting problems
- FPAUS
- FPRAS
- Non-approximability
- Single cut and join

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*Theoretical Computer Science*,

*552*(C), 83-98. https://doi.org/10.1016/j.tcs.2014.07.027

**Counting and sampling SCJ small parsimony solutions.** / Miklós, I.; Kiss, Sándor Z.; Tannier, Eric.

Research output: Contribution to journal › Article

*Theoretical Computer Science*, vol. 552, no. C, pp. 83-98. https://doi.org/10.1016/j.tcs.2014.07.027

}

TY - JOUR

T1 - Counting and sampling SCJ small parsimony solutions

AU - Miklós, I.

AU - Kiss, Sándor Z.

AU - Tannier, Eric

PY - 2014

Y1 - 2014

N2 - The Single Cut or Join (SCJ) operation on genomes, generalizing chromosome evolution by fusions and fissions, is the computationally simplest known model of genome rearrangement. While most genome rearrangement problems are already hard when comparing three genomes, it is possible to compute in polynomial time a most parsimonious SCJ scenario for an arbitrary number of genomes related by a binary phylogenetic tree.Here we consider the problems of sampling and counting the most parsimonious SCJ scenarios. We show that both the sampling and counting problems are easy for two genomes, and we relate SCJ scenarios to alternating permutations. However, for an arbitrary number of genomes related by a binary phylogenetic tree, the counting and sampling problems become hard. We prove that if a Fully Polynomial Randomized Approximation Scheme or a Fully Polynomial Almost Uniform Sampler exist for the most parsimonious SCJ scenario, then RP = NP.The proof has a wider scope than genome rearrangements: the same result holds for parsimonious evolutionary scenarios on any set of discrete characters.

AB - The Single Cut or Join (SCJ) operation on genomes, generalizing chromosome evolution by fusions and fissions, is the computationally simplest known model of genome rearrangement. While most genome rearrangement problems are already hard when comparing three genomes, it is possible to compute in polynomial time a most parsimonious SCJ scenario for an arbitrary number of genomes related by a binary phylogenetic tree.Here we consider the problems of sampling and counting the most parsimonious SCJ scenarios. We show that both the sampling and counting problems are easy for two genomes, and we relate SCJ scenarios to alternating permutations. However, for an arbitrary number of genomes related by a binary phylogenetic tree, the counting and sampling problems become hard. We prove that if a Fully Polynomial Randomized Approximation Scheme or a Fully Polynomial Almost Uniform Sampler exist for the most parsimonious SCJ scenario, then RP = NP.The proof has a wider scope than genome rearrangements: the same result holds for parsimonious evolutionary scenarios on any set of discrete characters.

KW - Computations on discrete structures

KW - Counting problems

KW - FPAUS

KW - FPRAS

KW - Non-approximability

KW - Single cut and join

UR - http://www.scopus.com/inward/record.url?scp=84926409923&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84926409923&partnerID=8YFLogxK

U2 - 10.1016/j.tcs.2014.07.027

DO - 10.1016/j.tcs.2014.07.027

M3 - Article

AN - SCOPUS:84926409923

VL - 552

SP - 83

EP - 98

JO - Theoretical Computer Science

JF - Theoretical Computer Science

SN - 0304-3975

IS - C

ER -