Counting and sampling SCJ small parsimony solutions

I. Miklós, Sándor Z. Kiss, Eric Tannier

Research output: Contribution to journalArticle

5 Citations (Scopus)

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 languageEnglish
Pages (from-to)83-98
Number of pages16
JournalTheoretical Computer Science
Volume552
Issue numberC
DOIs
Publication statusPublished - 2014

Fingerprint

Parsimony
Join
Counting
Genome Rearrangement
Genome
Genes
Sampling
Scenarios
Phylogenetic Tree
Binary Tree
Binary trees
Counting Problems
Polynomial
Arbitrary
Approximation Scheme
Chromosome
Polynomials
Polynomial time
Fusion
Permutation

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

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

In: Theoretical Computer Science, Vol. 552, No. C, 2014, p. 83-98.

Research output: Contribution to journalArticle

Miklós, I. ; Kiss, Sándor Z. ; Tannier, Eric. / Counting and sampling SCJ small parsimony solutions. In: Theoretical Computer Science. 2014 ; Vol. 552, No. C. pp. 83-98.
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