Title - Sorting by
Transpositions
An important problem in genome rearrangements is sorting
permutations by
transpositions. Its complexity is still open, and two rather
complicated
1.5-approximation algorithms for sorting linear permutations are
known
(Bafna and Pevzner, Christie). In this talk, we prove that the problem
of
sorting circular permutations by transpositions is equivalent to the
problem
of sorting linear permutations by transpositions. Hence, all
algorithms for
sorting linear permutations by transpositions can be used to
sort circular
permutations. Then, we derive our main result: A new
1.5-approximation
algorithm, which is considerably simpler than the previous
ones, and
achieves running time which is equal to the best known. The
analysis of the
algorithm is significantly less involved.
Joint
work with Ron Shamir
If time permits we will discuss briefly two
subsequent studies:
"A 1.375-approximation algorithm for
sorting by transpositions" (with Isaac Elias),
and "Matrix Tightness: A
Linear-Algebraic Framework for Sorting by Transpositions" (with Elad
Verbin).