The steady-states of splitter networks
<|reference_start|>The steady-states of splitter networks: 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.<|reference_end|>
@article{couëtoux2024the,
    title={The steady-states of splitter networks},
    author={Basile Cou"etoux and Bastien Gastaldi and Guyslain Naves},
    journal={arXiv preprint arXiv:2404.05472},
    year={2024},
    archivePrefix={arXiv},
    eprint={2404.05472},
    primaryClass={cs.DM}
}