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The Steady-States of Splitter Networks

Authors Basile Couëtoux, Bastien Gastaldi, Guyslain Naves

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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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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

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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References

  1. Václav E Beneš. On rearrangeable three-stage connecting networks. The Bell System Technical Journal, 41(5):1481-1492, 1962. Google Scholar
  2. Václav E Beneš. Permutation groups, complexes, and rearrangeable connecting networks. Bell System Technical Journal, 43(4):1619-1640, 1964. Google Scholar
  3. BoardGameGeek. Boardgame category: transportation. URL: https://boardgamegeek.com/boardgamecategory/1011/transportation.
  4. Bonnie S. Boardman and Caroline C. Krejci. Simulation of production and inventory control using the computer game factorio. In ASEE 2021 Gulf-Southwest Annual Conference, 2021. Google Scholar
  5. Basile Couëtoux, Bastien Gastaldi, and Guyslain Naves. The steady-states of splitter networks, 2024. URL: https://arxiv.org/abs/2404.05472.
  6. Chase Covello, Hyunjang Jung, and Bryan C. Watson. Using graph theory to investigate the role of expertise on infrastructure evolution: A case study examining the game factorio. In Conference on Systems Engineering Research, pages 297-311. Springer, 2023. Google Scholar
  7. Miguel Coviello Gonzalez and Marek Chrobak. Towards a theory of mixing graphs: A characterization of perfect mixability. Theoretical Computer Science, 845:98-121, 2020. Google Scholar
  8. Yefim A. Dinits. The method of scaling and transportation problems. Studies in Discrete Mathematics, Moscow, pages 46-57, 1973. Google Scholar
  9. Shivam Duhan, Chengming Zhang, Wenyu Jing, and Mingqi Li. Factory optimization using deep reinforcement learning ai. Purdue Undergraduate Research Conference, 57, 2019. Google Scholar
  10. Andrew V. Goldberg and Robert E. Tarjan. A new approach to the maximum-flow problem. Journal of the ACM (JACM), 35(4):921-940, 1988. Google Scholar
  11. Ketcheson, David. Mathematics Stackexchange: Belt Balancer problem (Factorio). URL: https://math.stackexchange.com/questions/1775378/belt-balancer-problem-factorio.
  12. Donald E Knuth. The Art of Computer Programming: Sorting and Searching, Volume 3. Pearson Education, 1998. Google Scholar
  13. Donald E. Knuth and Andrew C. Yao. The complexity of nonuniform random number generation. In JF Traub, editor, Algorithms and Complexity: New Directions and Recent Results, pages 357-428. Addison-Wesley, 1976. Google Scholar
  14. Legnagi, Alessandro and Montini, Axel. VeriFactory. URL: https://github.com/alegnagi/verifactory/.
  15. Andre Leue. Verification of Factorio Belt Balancers using Petri Nets. PhD thesis, Bachelorarbeit, Darmstadt, Technische Universität Darmstadt, 2021. Google Scholar
  16. MatthaeusHarris. Factorio belts are Turing-complete. URL: https://www.reddit.com/r/factorio/comments/lc25cx/factorio_belts_are_turing_complete/.
  17. Carol A. Meyers and Andreas S. Schulz. Integer equal flows. Operations Research Letters, 37(4):245-249, 2009. Google Scholar
  18. Amandeep Parmar. Integer programming approaches for equal-split network flow problems. PhD thesis, Georgia Institute of Technology, 2007. Google Scholar
  19. Sean Patterson, Joan Espasa, Mun See Chang, and Ruth Hoffmann. Towards automatic design of factorio blueprints. arXiv preprint arXiv:2310.01505, 2023. Google Scholar
  20. pocarski. Universal 8-8: Perfectly Balanced, as All Things Should Be. URL: https://web.archive.org/web/20230922022806/https://alt-f4.blog/ALTF4-27/.
  21. R-O-C-K-E-T. factorio-SAT: Enhancing the Factorio experience with SAT solvers. URL: https://github.com/R-O-C-K-E-T/Factorio-SAT.
  22. Kenneth N. Reid, Iliya Miralavy, Stephen Kelly, Wolfgang Banzhaf, and Cedric Gondro. The factory must grow: automation in factorio. In Proceedings of the Genetic and Evolutionary Computation Conference Companion, pages 243-244, 2021. Google Scholar
  23. K. Srinathan, Pranava R. Goundan, MVN Ashwin Kumar, R. Nandakumar, and C. Pandu Rangan. Theory of equal-flows in networks. In Computing and Combinatorics: 8th Annual International Conference, COCOON 2002 Singapore, August 15-17, 2002 Proceedings 8, pages 514-524. Springer, 2002. Google Scholar
  24. Wube Software. Factorio. URL: https://www.factorio.com/.
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