Canadian Distributed Mentorship Project Research Report

In this report, we propose an effective way to find the medians of three permutations by minimizing the number of pairwise disagreements under the Kendall-τ distance. The heuristic algorithms individually manipulate each of the starting three permutations by moving integers to the left or right within the permutation until no further moves can be executed. Then the Kendall-τ distance is measured on each of the three results, and those with the minimal distance are considered to be medians. When comparing the heuristic to the brute force, the heuristic algorithms have effectively reduced calculation times while maintaining accuracy.