LIPIcs.FUN.2024.9.pdf
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The Steady-States of Splitter Networks
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Guyslain Naves 
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12th International Conference on Fun with Algorithms (FUN 2024)
Series: Leibniz International Proceedings in Informatics (LIPIcs)
Conference: International Conference on Fun with Algorithms (FUN) - License:
Creative Commons Attribution 4.0 International license
- Publication Date: 2024-05-29
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Basile Couëtoux, Bastien Gastaldi, and Guyslain Naves. The Steady-States of Splitter Networks. In 12th International Conference on Fun with Algorithms (FUN 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 291, pp. 9:1-9:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
https://doi.org/10.4230/LIPIcs.FUN.2024.9
https://doi.org/10.4230/LIPIcs.FUN.2024.9
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 Ω(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.
Subject Classification
ACM Subject Classification
- Theory of computation → Network flows
- Mathematics of computing → Network flows
- Mathematics of computing → Graph algorithms
- Theory of computation → Random walks and Markov chains
Keywords
- Factorio
- splitter networks
- flow
- balancer
- steady-state
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