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.
@InProceedings{couetoux_et_al:LIPIcs.FUN.2024.9, author = {Cou\"{e}toux, Basile and Gastaldi, Bastien and Naves, Guyslain}, title = {{The Steady-States of Splitter Networks}}, booktitle = {12th International Conference on Fun with Algorithms (FUN 2024)}, pages = {9:1--9:14}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-314-0}, ISSN = {1868-8969}, year = {2024}, volume = {291}, editor = {Broder, Andrei Z. and Tamir, Tami}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FUN.2024.9}, URN = {urn:nbn:de:0030-drops-199174}, doi = {10.4230/LIPIcs.FUN.2024.9}, annote = {Keywords: Factorio, splitter networks, flow, balancer, steady-state} }
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