39 lines
1.4 KiB
TeX
39 lines
1.4 KiB
TeX
% GENERAL
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\newcommand{\PROBLEMname}[1]{\textrm{#1}}
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\newcommand{\PROBLEMinputs}{\mathcal{D}}
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\newcommand{\PROBLEMinput}{I}
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\newcommand{\PROBLEMsolution}{\sigma}
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\newcommand{\PROBLEMsolutionsFor}[1]{S(#1)}
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\newcommand{\PROBLEMsolutionsForInput}{\PROBLEMsolutionsFor{\PROBLEMinput}}
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\newcommand{\PROBLEMoptimalSolutionFor}[1]{\text{OPT}(#1)}
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\newcommand{\PROBLEMoptimalSolutionForInput}{\PROBLEMoptimalSolutionFor{\PROBLEMinput}}
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\newcommand{\PROBLEMinputLength}{|\PROBLEMinput|}
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\newcommand{\PROBLEMlength}{n}
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% REDUCTION
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\newcommand{\REDUCTION}[2]{$#1 \leq_{\textrm{T}} #2$}
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% GÜTE
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\newcommand{\GUETEguaranteedAlgo}[1]{\rho_{#1}}
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\newcommand{\GUETEguaranteed}{\GUETEguaranteedAlgo{\ALGOapprox}}
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\newcommand{\GUETEguaranteedForInput}{\GUETEguaranteed(\PROBLEMinput)}
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\newcommand{\GUETEguaranteedForLength}{\GUETEguaranteed(\PROBLEMlength)}
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\newcommand{\GUETEdeviance}{\rho'_\ALGOapprox}
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\newcommand{\GUETEworstCase}{\rho_A^{wc}}
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\newcommand{\GUETEworstCaseForLength}{\GUETEworstCase(\PROBLEMlength)}
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% ERRORS
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\newcommand{\ERRORrelative}{\epsilon_\ALGOapprox}
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\newcommand{\ERRORrelativeForLength}{\ERRORrelative(\PROBLEMlength)}
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% Traveling Salesman Problem
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\newcommand{\PROBLEMtsp}{\PROBLEMname{TSP}}
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\newcommand{\PROBLEMtspOfGuete}[1]{\PROBLEMtsp[#1]}
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\newcommand{\PROBLEMtspMetric}{\Delta\PROBLEMtsp}
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% Hamilton
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\newcommand{\PROBLEMhamilton}{\PROBLEMname{HAMILTON}}
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% Minimal Spanning Tree
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\newcommand{\PROBLEMmst}{MST} |