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\@writefile{toc}{\contentsline {section}{\numberline {1}Applications of Communication Complexity: Extended Formulations of Linear Programs}{1}}
\@writefile{toc}{\contentsline {section}{\numberline {2}Definitions and Background}{1}}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.1}The permutahedron polytope}{2}}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.2}Extended Formulations}{2}}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.3}Brief History}{3}}
\@writefile{toc}{\contentsline {section}{\numberline {3}Lower Bounds on Extension Complexity}{3}}
\@writefile{toc}{\contentsline {subsection}{\numberline {3.1}Yannakakis' Factorization Theorem}{3}}
\@writefile{toc}{\contentsline {subsection}{\numberline {3.2}The Clique Polytope}{4}}
\@writefile{toc}{\contentsline {section}{\numberline {4}Nonnegative Rank and Communication Complexity}{5}}
\@writefile{toc}{\contentsline {subsection}{\numberline {4.1}Extended Formulations for Approximate Linear Programs}{5}}
\@writefile{toc}{\contentsline {subsection}{\numberline {4.2}An Equivalent Communication Complexity Problem}{6}}