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Restructured from flat .tex/.pdf files into per-paper subdirectories. Added Antje Worring as co-author on all papers. Synced PDFs to pdfs/ for download site.
53 lines
1.9 KiB
TeX
53 lines
1.9 KiB
TeX
\section{Multi-Appchain Validator Economics}
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\label{sec:multiappchain}
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\subsection{Appchain Validation Cost-Benefit}
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Validating additional appchains incurs marginal hardware costs but generates additional rewards:
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\begin{definition}[Appchain Validation Profit]
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The marginal profit of validator $v_i$ adding appchain $k$ is:
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\begin{equation}
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\Delta\pi_{i,k} = r_{i,k}^{\text{appchain}} - h_k^{\text{marginal}}
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\end{equation}
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where $h_k^{\text{marginal}}$ is the incremental hardware cost (CPU, storage, bandwidth) for running appchain $k$'s VM.
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\end{definition}
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\begin{table}[H]
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\centering
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\caption{Estimated marginal costs and rewards for appchain validation.}
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\label{tab:appchain_economics}
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\begin{tabular}{lrrr}
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\toprule
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\textbf{Appchain Type} & \textbf{Marginal Cost/epoch} & \textbf{Reward/epoch} & \textbf{Net Profit} \\
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\midrule
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EVM (light usage) & 0.5 LUX & 2.0 LUX & +1.5 LUX \\
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EVM (heavy usage) & 2.0 LUX & 8.0 LUX & +6.0 LUX \\
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Custom VM (gaming) & 3.0 LUX & 5.0 LUX & +2.0 LUX \\
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Custom VM (DeFi) & 1.5 LUX & 10.0 LUX & +8.5 LUX \\
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\bottomrule
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\end{tabular}
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\end{table}
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\subsection{Optimal Appchain Portfolio}
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\begin{algorithm}[H]
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\caption{Optimal Appchain Selection for Validator $v_i$}
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\label{alg:appchain_selection}
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\begin{algorithmic}[1]
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\Require Available appchains $\mathcal{K}$, hardware capacity $H_i^{\max}$
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\State Sort appchains by $\Delta\pi_{i,k} / h_k^{\text{marginal}}$ (profit per cost)
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\State $\mathcal{K}_i \gets \emptyset$; $H_{\text{used}} \gets h_{\text{primary}}$
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\For{each appchain $k$ in sorted order}
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\If{$H_{\text{used}} + h_k^{\text{marginal}} \leq H_i^{\max}$ and $\Delta\pi_{i,k} > 0$}
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\State $\mathcal{K}_i \gets \mathcal{K}_i \cup \{k\}$
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\State $H_{\text{used}} \gets H_{\text{used}} + h_k^{\text{marginal}}$
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\EndIf
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\EndFor
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\State \Return $\mathcal{K}_i$
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\end{algorithmic}
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\end{algorithm}
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This is a variant of the fractional knapsack problem, solvable in $O(|\mathcal{K}| \log |\mathcal{K}|)$ time.
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