
\newcommand{\F}{\mathcal{F}}
\newcommand{\B}{\mathcal{B}}
\newcommand{\I}{\mathcal{I}}
\newcommand{\C}{\mathcal{C}}
\newcommand{\Hit}{\text{Hit}}
\newcommand{\HSGap}{\text{HSGap}}
\newcommand{\IntGap}{\text{IntGap}}
\newcommand{\OPTLP}{\text{OPTLP}}
\newcommand{\OPT}{\text{OPT}}
\newcommand{\DecRank}{\text{Rank-}k\text{-Reduction}}
\newcommand{\flats}{\operatorname{Flats}}
\newcommand{\cl}{\operatorname{cl}}
\newcommand{\gap}{\operatorname{gap}}
\newcommand{\igap}{\operatorname{igap}}
\newcommand{\cogirthratio}{\rho}
\newcommand{\cogirthratiowt}{\cogirthratio^{\mathrm{wt}}}
\newcommand{\strength}{\operatorname{strength}}
\newcommand{\argmin}{\operatorname{arg\,min}}
\newcommand{\argmax}{\operatorname{arg\,max}}
\newcommand{\del}{\setminus}
\newcommand{\con}{/}
\newcommand{\minor}{\times}
\newcommand{\floor}[1]{\left\lfloor #1 \right\rfloor}
\newcommand{\ceil}[1]{\left\lceil #1 \right\rceil}
\newcommand{\set}[1]{\left\{ #1 \right\}}
\newcommand{\norm}[1]{\left\| #1 \right\|}
\newcommand{\rm}[1]{\operatorname{#1}}
\newcommand{\mex}{\operatorname{mex}}
\newcommand{\lcm}{\operatorname{lcm}}
\newcommand{\dist}{\operatorname{dist}}
\newcommand{\poly}{\operatorname{poly}}
\newcommand{\polylog}{\operatorname{polylog}}
\newcommand{\span}{\operatorname{span}}