Approximation Algorithms for Sorting by Transpositions Problems

Tzvika Hartman

In this talk I'll present two works. The first considers the
problem
of sorting by transpositions and transreversals. We provide a
1.5-approximation algorithm for the problem, improving on a
five-years-old 1.75 ratio for this problem. Our algorithm is also faster
than current approaches and requires $O(n^{3/2} \sqrt{\log{n}})$ time
for $n$ genes.
Joint work with Roded Sharan.

The second work considers sorting by transpositions only. The
complexity of this problem is still open and it has been a ten-year-old
open problem to improve the best known 1.5-approximation algorithm. Here
we provide a 1.375-approximation algorithm. The algorithm is based on
new results regarding the diameter of three subsets of the symmetric
group: We determine the exact transposition diameter of 2-permutations
and simple permutations, and find an upper bound for the diameter of
3-permutations.
Joint work with Isaac Elias.