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The Steady-States of Splitter Networks

Authors Basile Couëtoux, Bastien Gastaldi, Guyslain Naves

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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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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.

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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

Author Details

Basile Couëtoux
  • Aix-Marseille Université, CNRS, LIS, Marseille, France
Bastien Gastaldi
  • Télécom SudParis, Institut Polytechnique de Paris, Evry, France
Guyslain Naves
  • Aix-Marseille Université, CNRS, LIS, Marseille, France

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