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RBDT: A Computerized Task System based in Transposition for the Continuous Analysis of Relational Behavior Dynamics in Humans

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A Barrier for Further Approximating Sorting by Transpositions.

Luiz A G Silva¹, Luis A B Kowada², Maria E M T Walter¹

¹Departamento de Ciência da Computação, Universidade de Brasília, Brasília, Brazil.

Journal of Computational Biology : a Journal of Computational Molecular Cell Biology

|October 26, 2023

Summary

This study determines the transposition distance for "palisades" permutations, providing the exact transposition diameter for 3-permutations (TD3). This resolves a long-standing problem and impacts approximation algorithms for genome rearrangements.

Keywords:

genome rearrangements sorting by transpositions transposition distance problem

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Area of Science:

Computational Biology
Genomics
Combinatorics

Background:

The transposition distance problem is fundamental in genome rearrangements.
Sorting by transpositions (SBT) is a key problem in this field.
Palisades are known to be difficult permutations for SBT.

Purpose of the Study:

To determine the transposition distance of palisades.
To provide the exact transposition diameter for 3-permutations (TD3).
To analyze the implications for approximation algorithms for SBT.

Main Methods:

Investigating palisades, a family of hard-to-sort permutations.
Calculating transposition distances for these permutations.
Utilizing the Bafna-Pevzner lower bound.

Main Results:

The exact transposition diameter for 3-permutations (TD3) was determined.
It was shown that approximation ratios for SBT cannot be guaranteed below 1.375 using the Bafna-Pevzner lower bound.
This finding has significant implications for the study of SBT.

Conclusions:

The transposition distance of palisades has been precisely calculated.
The exact value for TD3 has been established, resolving a known gap in research.
The study provides crucial insights into the limitations of approximation algorithms for sorting by transpositions.