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\relax
\@ writefile{ toc} { \contentsline { section} { \numberline { 1} Introduction} { 1} { } \protected @file@percent }
\@ writefile{ toc} { \contentsline { subsection} { \numberline { 1.1} Context} { 1} { } \protected @file@percent }
\@ writefile{ toc} { \contentsline { subsection} { \numberline { 1.2} Formal description of the problem} { 1} { } \protected @file@percent }
\newlabel { eq:optimal} { { { OPT} } { 1} }
\@ writefile{ toc} { \contentsline { section} { \numberline { 2} Properties of an optimal 3-strict assignment} { 2} { } \protected @file@percent }
\@ writefile{ toc} { \contentsline { subsection} { \numberline { 2.1} Optimal assignment} { 2} { } \protected @file@percent }
\newlabel { sec:opt_ assign} { { 2.1} { 2} }
\@ writefile{ lof} { \contentsline { figure} { \numberline { 1} { \ignorespaces On the left, the creation of a concrete assignment with the naive approach of repeating tokens. On the right, the zones containing the nodes.} } { 4} { } \protected @file@percent }
\@ writefile{ toc} { \contentsline { subsection} { \numberline { 2.2} Minimal transfer} { 5} { } \protected @file@percent }
\newlabel { hyp:A} { { { H3A} } { 5} }
\newlabel { hyp:B} { { { H3B} } { 5} }
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\@ writefile{ lof} { \contentsline { figure} { \numberline { 2} { \ignorespaces Flow problem to compute and optimal assignment.} } { 5} { } \protected @file@percent }
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\@ writefile{ toc} { \contentsline { subsubsection} { \numberline { A)} Minimizing the zone discrepancy} { 6} { } \protected @file@percent }
\@ writefile{ lof} { \contentsline { figure} { \numberline { 3} { \ignorespaces On the left: the graph $ G _ T $ encoding an assignment to minimize the zone discrepancy. On the right: the graph $ G _ T $ encoding an assignment to minimize the node discrepancy.} } { 7} { } \protected @file@percent }
\@ writefile{ toc} { \contentsline { subsubsection} { \numberline { B)} Minimizing the node discrepancy} { 8} { } \protected @file@percent }
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\@ writefile{ toc} { \contentsline { subsubsection} { \numberline { C)} Linear combination of both criteria} { 9} { } \protected @file@percent }
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\@ writefile{ toc} { \contentsline { subsection} { \numberline { 2.3} Algorithm} { 9} { } \protected @file@percent }
\@ writefile{ loa} { \contentsline { algorithm} { \numberline { 1} { \ignorespaces Optimal 3-strict assignment} } { 9} { } \protected @file@percent }
\newlabel { alg:total} { { 1} { 9} }
\@ writefile{ loa} { \contentsline { algorithm} { \numberline { 2} { \ignorespaces Computation of the optimal utilization} } { 10} { } \protected @file@percent }
\newlabel { alg:util} { { 2} { 10} }
\newlabel { lin:subutil} { { 2} { 10} }
\newlabel { lin:loopsub} { { 3} { 10} }
\newlabel { lin:findmin} { { 4} { 10} }
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\@ writefile{ loa} { \contentsline { algorithm} { \numberline { 3} { \ignorespaces Computation of a candidate assignment} } { 11} { } \protected @file@percent }
\newlabel { alg:opt} { { 3} { 11} }
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\@ writefile{ loa} { \contentsline { algorithm} { \numberline { 4} { \ignorespaces Minimization of the number of transfers} } { 11} { } \protected @file@percent }
\newlabel { alg:mini} { { 4} { 11} }
\newlabel { lin:repeat} { { 3} { 11} }
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\@ writefile{ toc} { \contentsline { section} { \numberline { 3} Computation of a 3-non-strict assignment} { 11} { } \protected @file@percent }
\@ writefile{ toc} { \contentsline { subsection} { \numberline { 3.1} Choices of optimality} { 11} { } \protected @file@percent }
\@ writefile{ toc} { \contentsline { subsection} { \numberline { 3.2} Computation of a candidate assignment} { 11} { } \protected @file@percent }
\@ writefile{ toc} { \contentsline { subsection} { \numberline { 3.3} Maximal spread and minimal transfers} { 12} { } \protected @file@percent }
\gdef \@ abspage@last{ 13}