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Sorting signed circular permutations by super short operations.

Andre R Oliveira1, Guillaume Fertin2, Ulisses Dias3

  • 11Institute of Computing, University of Campinas, Campinas, Brazil.

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|August 2, 2018
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Summary
This summary is machine-generated.

This study introduces a novel cyclic permutation graph to solve the previously unsolved problem of sorting signed circular permutations using super short reversals and transpositions. A polynomial algorithm is presented, advancing computational biology and genome rearrangement research.

Keywords:
Circular permutationsGenome rearrangementsSuper short operations

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Area of Science:

  • Computational Biology
  • Genomics
  • Bioinformatics

Background:

  • Genome rearrangements are crucial for estimating evolutionary distances.
  • Genomes are modeled as signed permutations, with sorting by reversals and transpositions being key problems.
  • Super short operations (SSOs) involve rearrangements of at most two genes.

Purpose of the Study:

  • To address the open problem of sorting signed circular permutations by super short reversals and transpositions.
  • To develop a polynomial-time algorithm for this specific genome rearrangement problem.

Main Methods:

  • Introduction of a new graph structure: the cyclic permutation graph.
  • Development of intermediate results using this graph.
  • Design of a polynomial algorithm based on the new graph structure.

Main Results:

  • A polynomial algorithm is designed for sorting signed circular permutations by super short reversals and transpositions.
  • This fills a gap in the computational complexity landscape of SSO problems.

Conclusions:

  • The developed algorithm provides an efficient solution for a previously intractable problem in genome rearrangement.
  • The cyclic permutation graph is a valuable tool for analyzing circular permutations in computational biology.