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Published in:
2009 | OriginalPaper | Chapter
Sorting Signed Permutations by Inversions in O(nlogn) Time
Authors : Krister M. Swenson, Vaibhav Rajan, Yu Lin, Bernard M. E. Moret
Published in: Research in Computational Molecular Biology
Publisher: Springer Berlin Heidelberg
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The study of genomic inversions (or reversals) has been a mainstay of computational genomics for nearly 20 years. After the initial breakthrough of Hannenhalli and Pevzner, who gave the first polynomial-time algorithm for sorting signed permutations by inversions, improved algorithms have been designed, culminating with an optimal linear-time algorithm for computing the inversion distance and a subquadratic algorithm for providing a shortest sequence of inversions—also known as sorting by inversions. Remaining open was the question of whether sorting by inversions could be done in
O
(
n
log
n
) time.
In this paper, we present a qualified answer to this question, by providing two new sorting algorithms, a simple and fast randomized algorithm and a deterministic refinement. The deterministic algorithm runs in time
O
(
n
log
n
+
kn
), where
k
is a data-dependent parameter. We provide the results of extensive experiments showing that both the average and the standard deviation for
k
are small constants, independent of the size of the permutation. We conclude (but do not prove) that almost all signed permutations can be sorted by inversions in
O
(
n
log
n
) time.