# Two Independent and Highly Efficient Open Source TKF91 Implementations

## TL;DR

This paper presents two open-source implementations of the TKF91 algorithm, developed by students during a programming course, which are efficient and produce consistent results.

## Contribution

Two independent, optimized, and numerically stable open-source implementations of the TKF91 algorithm are introduced.

## Key findings

- The two implementations yield identical results with minor numerical deviations, confirming their correctness.
- Optimizations applied by the student teams are described and made publicly available.
- The implementations are intended to benefit the scientific community and educational programming courses.

## Abstract

In the context of a master level programming practical at the computer science department of the Karlsruhe Institute of Technology, we developed and make available two independent and highly optimized open-source implementations for the pair-wise statistical alignment model, also known as TKF91, that was developed by Thorne, Kishino, and Felsenstein in 1991. This paper has two parts. In the educational part, we cover teaching issues regarding the setup of the course and the practical and summarize student and teacher experiences. In the scientific part, the two student teams (Team I: Nikolai, Sebastian, Daniel; Team II: Sarah, Pierre) present their solutions for implementing efficient and numerically stable implementations of the TKF91 algorithm. The two teams worked independently on implementing the same algorithm. Hence, since the implementations yield identical results —with slight numerical deviations— we are confident that the implementations are correct. We describe the optimizations applied and make them available as open-source codes in the hope that our findings and software will be useful to the community as well as for similar programming practicals at other universities.