[{"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","scopus_import":"1","author":[{"full_name":"Breitkopf, Tom-Lukas","last_name":"Breitkopf","first_name":"Tom-Lukas"},{"full_name":"Dallot, Julien","last_name":"Dallot","first_name":"Julien"},{"first_name":"Antoine","orcid":"0000-0003-4268-7368","id":"888a098e-fcac-11ee-aff7-d347be57b725","last_name":"El-Hayek","full_name":"El-Hayek, Antoine"},{"first_name":"Stefan","full_name":"Schmid, Stefan","last_name":"Schmid"}],"citation":{"mla":"Breitkopf, Tom-Lukas, et al. “Ranking Opinions with Few States in Population Protocols.” <i>Proceedings of the ACM Symposium on Principles of Distributed Computing</i>, Association for Computing Machinery, 2026, pp. 414–24, doi:<a href=\"https://doi.org/10.1145/3796701.3815913\">10.1145/3796701.3815913</a>.","ama":"Breitkopf T-L, Dallot J, El-Hayek A, Schmid S. Ranking opinions with few states in population protocols. In: <i>Proceedings of the ACM Symposium on Principles of Distributed Computing</i>. Association for Computing Machinery; 2026:414-424. doi:<a href=\"https://doi.org/10.1145/3796701.3815913\">10.1145/3796701.3815913</a>","short":"T.-L. Breitkopf, J. Dallot, A. El-Hayek, S. Schmid, in:, Proceedings of the ACM Symposium on Principles of Distributed Computing, Association for Computing Machinery, 2026, pp. 414–424.","apa":"Breitkopf, T.-L., Dallot, J., El-Hayek, A., &#38; Schmid, S. (2026). Ranking opinions with few states in population protocols. In <i>Proceedings of the ACM Symposium on Principles of Distributed Computing</i> (pp. 414–424). Egham, United Kingdom: Association for Computing Machinery. <a href=\"https://doi.org/10.1145/3796701.3815913\">https://doi.org/10.1145/3796701.3815913</a>","ista":"Breitkopf T-L, Dallot J, El-Hayek A, Schmid S. 2026. Ranking opinions with few states in population protocols. Proceedings of the ACM Symposium on Principles of Distributed Computing. PODC: Symposium on Principles of Distributed Computing, 414–424.","chicago":"Breitkopf, Tom-Lukas, Julien Dallot, Antoine El-Hayek, and Stefan Schmid. “Ranking Opinions with Few States in Population Protocols.” In <i>Proceedings of the ACM Symposium on Principles of Distributed Computing</i>, 414–24. Association for Computing Machinery, 2026. <a href=\"https://doi.org/10.1145/3796701.3815913\">https://doi.org/10.1145/3796701.3815913</a>.","ieee":"T.-L. Breitkopf, J. Dallot, A. El-Hayek, and S. Schmid, “Ranking opinions with few states in population protocols,” in <i>Proceedings of the ACM Symposium on Principles of Distributed Computing</i>, Egham, United Kingdom, 2026, pp. 414–424."},"abstract":[{"lang":"eng","text":"Population protocols are a model of distributed computing where\r\n𝑛 agents, each a simple finite-state machine, interact in pairs to\r\nsolve a common task against a (adversarial) interaction scheduler.\r\nThis model was intensively studied in recent years; in particular,\r\nthe problem of relative majority received much attention: Each\r\nagent starts with an input opinion (or color) out of 𝑘 possibilities,\r\nand the goal is for each agent to eventually output the color with\r\nthe largest support in the population. Before our work, the state\r\ncomplexity (the minimum number of states required per agent) was\r\nonly known to be between Ω(𝑘\r\n2\r\n) and𝑂(𝑘\r\n7\r\n). Our main contribution\r\nis a population protocol that solves the relative majority problem\r\nwith 𝑘\r\n3\r\nstates. We achieve this result with a new protocol called\r\nCircles. While prior approaches in the literature relied on duels of\r\nagents to find the majority color — an approach that proved effective\r\nfor the case with two colors — Circles partitions the agents into\r\ncircular linked lists of decreasing sizes, with the property that no\r\ntwo agents with the same initial color lie in the same circle. We\r\nshow that Circles always correctly computes the desired structure\r\nagainst the most adversarial of schedulers (weakly fair). We then\r\nshow that a trivial extension of Circles solves the relative majority\r\nproblem. We extend our protocol to handle various tie-breaking\r\nmechanisms or to support the case where the agents do not share a\r\nprior ordering of the colors. Finally, we show that a modification of\r\nCircles solves the ranking problem with 2 · 𝑘^4\r\nstates, where each\r\nagent must output the rank of its initial color in the population."}],"tmp":{"image":"/images/cc_by.png","short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"article_processing_charge":"Yes","date_created":"2026-07-14T05:40:17Z","publication_status":"published","file_date_updated":"2026-07-16T11:18:44Z","quality_controlled":"1","publication":"Proceedings of the ACM Symposium on Principles of Distributed Computing","title":"Ranking opinions with few states in population protocols","corr_author":"1","conference":{"name":"PODC: Symposium on Principles of Distributed Computing","end_date":"2026-07-10","start_date":"2026-07-06","location":"Egham, United Kingdom"},"day":"01","date_published":"2026-07-01T00:00:00Z","month":"07","year":"2026","page":"414 - 424","has_accepted_license":"1","doi":"10.1145/3796701.3815913","publisher":"Association for Computing Machinery","acknowledgement":"Funded by the European union. Views and opinions expressed are\r\nhowever those of the author(s) only and do not necessarily reflect\r\nthose of the European Union or the European Research Council\r\nExecutive Agency. Neither the European Union nor the granting authority can be held responsible for them. This project has received\r\nfunding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme\r\n(MoDynStruct, No. 101019564) and the Austrian Science\r\nFund (FWF) grant DOI 10.55776/I5982. For open access purposes,\r\nthe author has applied a CC BY public copyright license to any\r\nauthor-accepted manuscript version arising from this submission.","supplementarymaterial":"no","OA_type":"gold","das_tickbox":"0","oa_version":"Published Version","type":"conference","project":[{"call_identifier":"H2020","grant_number":"101019564","_id":"bd9ca328-d553-11ed-ba76-dc4f890cfe62","name":"The design and evaluation of modern fully dynamic data structures"},{"grant_number":"I05982","name":"Static and Dynamic Hierarchical Graph Decompositions","_id":"bda196b2-d553-11ed-ba76-8e8ee6c21103"}],"researchdata_availability":"no","external_id":{"arxiv":["2605.18707"]},"ec_funded":1,"department":[{"_id":"MoHe"},{"_id":"GradSch"}],"OA_place":"publisher","file":[{"checksum":"e56da70c1b2e7e663d2d8106cf07a30a","relation":"main_file","date_updated":"2026-07-16T11:18:44Z","creator":"dernst","content_type":"application/pdf","file_id":"22353","date_created":"2026-07-16T11:18:44Z","file_size":702140,"file_name":"2026_ACMPODC_Breitkopf.pdf","access_level":"open_access","success":1}],"arxiv":1,"publication_identifier":{"isbn":["9798400725128"]},"ddc":["000"],"date_updated":"2026-07-16T11:19:52Z","_id":"22327","language":[{"iso":"eng"}],"status":"public","oa":1}]