@@ -93,7 +93,7 @@ This is a bit of a mouthful to work with, so it may help to simply approximate t

\begin{enumerate}

\item Design an algorithm (or algorithms!) that given a permutation $\pi$ as input, implements $\pi$ using weighted reversals on the path.

\item Give a bound on the runtime of the algorithm.

\item Compare with the best known algorithm called odd-even sort~\cite{Knuth1998}, which takes time $n-o(n)$. If we beat it, hooray!

\item Compare with the best known algorithm called odd-even sort~\cite{Knuth1998}, which takes time $n-o(n)$. If we beat it, hooray!

\item If we cannot beat the odd-even sort, then we try to show a runtime lower bound of $n-o(n)$.

\end{enumerate}

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@@ -109,5 +109,7 @@ This is a bit of a mouthful to work with, so it may help to simply approximate t

\item How much time does a weighted reversal require in a model that only allows swaps?

\item Using this information, can you give a lower bound on the routing time using weighted reversals?

\end{enumerate}

Permutation via weighted reversal has been studied in the context of gene sequencing. Here are some potentially useful references, \cite{Bender2008, Pinter2002, Blanchette1996}. Note that in that context, the time cost is once again the time for all operations, while we are interesting in parallelizing non-overlapping reversals as much as possible.