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\title{Approximation Algorithms for Sparsest Cut}
\author{Class 4. \zh{丛宇}, 202411081537\\ Major: Theoretical Computer Science}
\date{}

\DeclareMathOperator*{\opt}{OPT}
\DeclareMathOperator*{\len}{len}
\def\scut{\textsc{Sparsest Cut}}
\def\nonuscut{\textsc{Non-Uniform Sparsest Cut}}

\begin{document}
\maketitle

\paragraph{Research problem} What is the best possible approximation rate of linear programming based approximation algorithms for \scut? What about algorithms for planar graphs?

\section{Introduction}
% Requirement: The introduction may have the following parts: 
% Establishing the importance (Background), 
% literature review (previous research contributions)
% Gap/the specific problem
% The present study (the research topic, the research purpose  )
% The information should be presented in coherent paragraphs.

\section{Literature Review}
% Requirement: summarize previous research contributions and identify the gap or the specific problem

\section{The Research Design}
% Requirement : Your research design may include exact details of your design and the information should be presented in coherent paragraphs:
% Example:
% Research type: e.g. qualitative study, using primary data
% Sources and other important details 
% Research methods: e.g. Questionnaire surveys and interviews
% Possible difficulties/ problems or issues worth considering 
% Data analysis (the specific data analysis method)
% e.g. Using SPSS to analyze the survey data and Using NVivo to analyze the interview data (details of the method and reasons for the choice)
% The significance/ implications of the study
  

\section{Time Table}
% Data collection: e.g. During the program and first 6 months after the program (Aug. 2023- May. 2024)
% Data analysis: June 2024- Sept. 2024


\scut{} and \nonuscut{} \citep{chalermsook_approximating_2024}
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