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papers/lux-market-nft/sections/05-liquidity-aggregation.tex
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\section{Liquidity Aggregation}
\subsection{Marketplace Integration}
Lux.market aggregates liquidity from major marketplaces:
\begin{table}[h]
\centering
\begin{tabular}{|l|c|c|c|}
\hline
\textbf{Marketplace} & \textbf{Fee} & \textbf{Volume Share} & \textbf{Fill Rate} \\
\hline
OpenSea & 2.5\% & 45\% & 92\% \\
LooksRare & 2.0\% & 12\% & 88\% \\
X2Y2 & 0.5\% & 8\% & 85\% \\
Blur & 0\% & 25\% & 90\% \\
Rarible & 2.5\% & 5\% & 82\% \\
Others & Variable & 5\% & 75\% \\
\hline
\end{tabular}
\caption{Marketplace integration metrics}
\end{table}
\subsection{Unified Order Book}
The unified order book maintains:
\begin{equation}
O_{unified} = \bigcup_{m \in M} O_m \setminus O_{expired}
\end{equation}
with real-time updates via WebSocket connections:
\begin{lstlisting}[language=Solidity]
// WebSocket subscription for order updates
ws.subscribe({
type: 'orders',
collection: collectionAddress,
events: ['new', 'cancelled', 'filled']
});
\end{lstlisting}
\subsection{Best Price Routing}
The routing algorithm optimizes for:
\begin{equation}
\min \left( P_{total} = P_{listing} + F_{platform} + G_{estimated} + S_{slippage} \right)
\end{equation}
Subject to constraints:
\begin{align}
G_{estimated} &\leq G_{max} \\
S_{slippage} &\leq S_{tolerance} \\
T_{execution} &\leq T_{deadline}
\end{align}