% 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}}