Commit b7478ea9 authored by Aniruddha Bapat's avatar Aniruddha Bapat
Browse files

Added three refernces from weighted reversals in biology

parent 6e0aaeb6
......@@ -11,3 +11,45 @@
}
@Comment{jabref-meta: databaseType:biblatex;}
@InBook{Knuth1998,
author = {Donald E. Knuth},
title = {Networks for Sorting},
booktitle = {The Art of Computer Programming: Volume 3: Sorting and Searching (2nd Edition)},
year = {1998},
publisher = {Addison-Wesley Professional},
isbn = {0201896850},
pages = {219--247},
}
@article{Bender2008,
title={Improved bounds on sorting by length-weighted reversals},
author={Bender, Michael A and Ge, Dongdong and He, Simai and Hu, Haodong and Pinter, Ron Y and Skiena, Steven and Swidan, Firas},
journal={Journal of Computer and System Sciences},
volume={74},
number={5},
pages={744--774},
year={2008},
publisher={Elsevier}
}
@article{Pinter2002,
title={Genomic sorting with length-weighted reversals},
author={Pinter, Ron Y and Skiena, Steven},
journal={Genome Informatics},
volume={13},
pages={103--111},
year={2002},
publisher={Japanese Society for Bioinformatics}
}
@article{Blanchette1996,
title={Parametric genome rearrangement},
author={Blanchette, Mathieu and Kunisawa, Takashi and Sankoff, David},
journal={Gene},
volume={172},
number={1},
pages={GC11--GC17},
year={1996},
publisher={Elsevier}
}
......@@ -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}
......@@ -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.
\printbibliography%
\end{document}
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