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arXiv · 2404.05472

The steady-states of splitter networks

Basile Couëtoux·Bastien Gastaldi·Guyslain Naves
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Abstract

We introduce splitter networks, which abstract the behavior of conveyor belts found in the video game Factorio. Based on this definition, we show how to compute the steady-state of a splitter network. Then, leveraging insights from the players community, we provide multiple designs of splitter networks capable of load-balancing among several conveyor belts, and prove that any load-balancing network on $n$ belts must have $\Omega(n \log n)$ nodes. Incidentally, we establish connections between splitter networks and various concepts including flow algorithms, flows with equality constraints, Markov chains and the Knuth-Yao theorem about sampling over rational distributions using a fair coin.

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Basile Couëtoux, Bastien Gastaldi, Guyslain Naves. 2024-04-08. The steady-states of splitter networks. https://arxiv.org/abs/2404.05472

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