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\title{When Asymptotic Complexity Fails: An Empirical and Cost-Based Study of Binary and Fibonacci Heaps in Python}
\author{Seungjun Lee}
\date{\today}

\begin{document}

\maketitle

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\tableofcontents

\newpage

\section{Introduction}
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\newpage
\section{Background}

\subsection{Dijkstra's algorithm}

\subsubsection*{Time Complexity}

\subsection{Priority queue}

\subsubsection*{Time Complexity}

\subsection{Runtime}

\newpage
\section{Methodology}

\subsection{Experimental Environment}

\subsection{Real data}

\subsection{Synthetic Graph Generation }

\subsection{Analysis Strategy}

\subsubsection{Decrease-key call count modeling}

\subsubsection{Operation unit cost modeling}

\subsubsection{Integrated prediction}

\subsection{Validation Metrics}

\newpage
\section{Results}

\subsection{Real data properties}

\subsection{Decrease-key Call Number Prediction}

\subsection{Operation Unit Cost Analysis}

\subsection{Integrated Runtime Prediction}

\newpage
\section{Discussion}

\subsection{Phase Transition as Regime Boundary}

\subsection{Cache Effects in Unit Cost}

\subsection{Asymptotic vs Empirical Cost}

\subsection{Limitations}


\newpage
\section{Conclustion}

\subsection{Summary of Contributions}

\subsection{Practical Implications}

\subsection{Future Work}

\end{document}