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A new 1.375-approximation algorithm for sorting by transpositions.

Luiz Augusto G Silva1, Luis Antonio B Kowada2, Noraí Romeu Rocco3

  • 1Departmento de Ciência da Computação, Universidade de Brasília, Brasília, Brazil. laugustogarcia@gmail.com.

Algorithms for Molecular Biology : AMB
|January 16, 2022
PubMed
Summary
This summary is machine-generated.

Sorting by transpositions (SBT) is a genome rearrangement problem. A new algorithm improves upon the Elias-Hartman algorithm, ensuring a 1.375 approximation ratio for sorting by transpositions.

Keywords:
Approximation algorithmsGenome rearrangementsSorting by TranspositionsTransposition Distance Problem

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Area of Science:

  • Computational Biology
  • Bioinformatics
  • Genomics

Background:

  • Sorting by transpositions (SBT) is a fundamental problem in genome rearrangements.
  • The problem is NP-hard, with the best prior approximation algorithm achieving a 1.375 ratio.
  • Existing algorithms use simplification techniques to reduce permutation complexity, but these can introduce inaccuracies.

Purpose of the Study:

  • To address limitations in the Elias-Hartman (EH) algorithm's simplification process for sorting by transpositions.
  • To develop a new approximation algorithm for SBT that guarantees the 1.375 approximation ratio.
  • To establish a new upper bound for transposition distance using an algebraic approach.

Main Methods:

  • Developed a novel algebraic approach to derive a new upper bound for transposition distance.
  • Designed a new approximation algorithm to overcome identified issues in the EH algorithm's simplification step.
  • Implemented and compared the new algorithm against the EH algorithm using extensive permutation testing.

Main Results:

  • The EH algorithm was found to exceed the 1.375 approximation ratio for permutations larger than size 7.
  • The new algorithm consistently maintains the 1.375 approximation ratio across tested permutations.
  • Experimental results show slightly improved distance calculations and comparable running times for the new algorithm.

Conclusions:

  • The proposed algorithm effectively solves sorting by transpositions, ensuring the 1.375 approximation ratio.
  • The new algorithm offers a more reliable solution compared to the EH algorithm, especially for larger permutations.
  • Further analysis indicates comparable performance and running times between the implemented algorithms.