initial commit

presentation/resources/macros.tex

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+% Math
+\renewcommand{\vec}[1]{\bm{#1}}
+\newcommand{\mathtuple}[1]{\left<#1\right>}
+\DeclareMathOperator\cost{cost}
+\DeclareMathOperator\edgeCost{c}
+\DeclareMathOperator\minimum{min}
+\DeclareMathOperator\cheapest{billigst}
+\DeclareMathOperator\nodeDegree{deg}
+
+% Some colors
+\definecolor{darkpastelgreen}{rgb}{0.01, 0.75, 0.24}
+
+
+
+
+% TikZ
+\tikzstyle{thickArrow}=[line width=1mm, draw=black,-triangle 45,postaction={draw, line width=3mm, shorten >=4mm, -}]
+% Allowes to draw a line parallel to an edge
+% Example:
+% 1. Declare a style in your graph: parallel/.style={decoration={sl,raise=-.75mm},decorate}
+% 2. Use the style: \draw[-,parallel] (a) to (b);
+%    This draws a line parallel to the edge a--b
+\pgfdeclaredecoration{sl}{initial}{
+	\state{initial}[width=\pgfdecoratedpathlength-1sp]{
+		\pgfmoveto{\pgfpointorigin}
+	}
+	\state{final}{
+		\pgflineto{\pgfpointorigin}
+	}
+}
+
+
+
+% Beamer
+\newcommand{\pageItemNote}[2]{
+	\only<#1>{
+		\note{
+			\begin{itemize}
+				#2
+			\end{itemize}
+		}
+	}
+}
+\newcommand{\pageNote}[2]{
+	\only<#1>{
+		\note{
+			#2
+		}
+	}
+}

presentation/resources/problems.tex

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

presentation/resources/symbols.tex

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+% GENERAL
+\newcommand{\mathset}[1]{\vec{#1}}
+\newcommand{\numbersystem}[1]{\mathbb{#1}}
+
+\newcommand{\numbersystemNatural}{\numbersystem{N}}
+\newcommand{\numbersystemReal}{\numbersystem{R}}
+
+\newcommand{\optimalTour}{R^*}
+\newcommand{\tour}{R}
+
+
+% Limit-Notation
+\newcommand{\LIMITbigO}{O}
+\newcommand{\LIMITbigOmega}{\Omega}
+\newcommand{\LIMITbigTheta}{\Theta}
+
+% NP / P
+\newcommand{\NPnotP}{\textrm{NP} \not= \textrm{P}}
+
+% Algorithms
+\newcommand{\ALGOapprox}{A}
+\newcommand{\ALGOapproxSolutionForI}{\ALGOapprox(\PROBLEMinput)}
+
+% Graphs
+\newcommand{\GRAPHfullyConnected}[1]{K_{#1}}
+\newcommand{\GRAPHedges}{\vec{E}}
+\newcommand{\GRAPHedgesCount}{|\GRAPHedges|}
+\newcommand{\GRAPHvertices}{\vec{V}}
+\newcommand{\GRAPHverticesCount}{|\GRAPHvertices|}
+\newcommand{\GRAPHcost}{c}
+\newcommand{\GRAPHcostOf}[2]{\GRAPHcost({#1},{#2})}
+\DeclareMathOperator{\GRAPHneighbors}{\bm{\Gamma}}
+
+% Insert-Heuristics
+\DeclareMathOperator\EH{EH}
+
+% Christofides
+\DeclareMathOperator\CH{CH}
+
+% Vertexcolor
+\newcommand{\GREEDYISstep}{t}
+\DeclareMathOperator\GREEDYISdelete{lösch}
+\newcommand{\GREEDYISdeletionStepSize}{\gamma_\GREEDYISstep}
+\newcommand{\GREEDYISdeletedStepGoodNodes}{\kappa_\GREEDYISstep}
+\newcommand{\GREEDYISnodeWithSmallestDeg}{u_\GREEDYISstep}
+\newcommand{\GREEDYISindependentSet}{\vec{U}}
+\newcommand{\GREEDYISindependentSetCount}{|\GREEDYISindependentSet|}
+\newcommand{\GREEDYISoptimalIndependentSet}{\GREEDYISindependentSet^*}
+\newcommand{\GREEDYISoptimalIndependentSetCount}{|\GREEDYISoptimalIndependentSet|}
+
+
+
+% Impossibletsp
+\newcommand{\IMPOSSIBLETSPguete}{r}
+
+
+
+%-------------
+% Algo-Names
+%-------------
+
+% GreedyIS
+\newcommand{\ALGOgreedyIS}{\textsc{GreedyIS}}
+% GreedyCol
+\newcommand{\ALGOgreedyColor}{\textsc{GreedyCol}}
+% GreedyCol2
+\newcommand{\ALGOgreedyColorTwo}{\textsc{GreedyCol2}}