\relax 
\@writefile{toc}{\contentsline {section}{\numberline {1}Preliminaries}{1}}
\@writefile{toc}{\contentsline {subsection}{\numberline {1.1}The Problem}{1}}
\@writefile{toc}{\contentsline {subsection}{\numberline {1.2}Optimal Strategies}{1}}
\newlabel{lem:swapping}{{2}{1}}
\newlabel{col:shortest}{{3}{1}}
\citation{lovasz1}
\newlabel{lem:multiplication}{{4}{2}}
\newlabel{lem:summing}{{5}{2}}
\@writefile{toc}{\contentsline {section}{\numberline {2}Symmetric Bimonotone Cost-Vectors}{2}}
\newlabel{lem:101}{{7}{2}}
\@writefile{toc}{\contentsline {section}{\numberline {3}Reversing Permutations by Swaps of Decreasing Weights}{3}}
\@writefile{toc}{\contentsline {subsection}{\numberline {3.1}General Observations}{3}}
\newlabel{steps}{{9}{3}}
\@writefile{toc}{\contentsline {subsection}{\numberline {3.2}Decreasing and Non-increasing Weights}{3}}
\bibcite{lovasz1}{Lo04}
\newlabel{r-l}{{13}{5}}