[{"quality_controlled":"1","file_date_updated":"2026-07-21T07:31:29Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","file":[{"date_created":"2026-07-21T07:31:29Z","success":1,"file_name":"2026_ACMPODC_dArchivio.pdf","creator":"dernst","access_level":"open_access","relation":"main_file","content_type":"application/pdf","file_id":"22379","date_updated":"2026-07-21T07:31:29Z","file_size":824239,"checksum":"e8208393a016d8e71d7b26c402045488"}],"doi":"10.1145/3796701.3815922","citation":{"short":"N. D’Archivio, H. Almahmoud, E. Natale, F. Mallmann-Trenn, in:, Proceedings of the Annual ACM Symposium on Principles of Distributed Computing, Association for Computing Machinery, 2026, pp. 425–436.","ista":"D’Archivio N, Almahmoud H, Natale E, Mallmann-Trenn F. 2026. Order statistics in population protocols via simple dynamics. Proceedings of the Annual ACM Symposium on Principles of Distributed Computing. PODC: Symposium on Principles of Distributed Computing, 425–436.","apa":"D’Archivio, N., Almahmoud, H., Natale, E., &#38; Mallmann-Trenn, F. (2026). Order statistics in population protocols via simple dynamics. In <i>Proceedings of the Annual ACM Symposium on Principles of Distributed Computing</i> (pp. 425–436). Egham, United Kingdom: Association for Computing Machinery. <a href=\"https://doi.org/10.1145/3796701.3815922\">https://doi.org/10.1145/3796701.3815922</a>","ama":"D’Archivio N, Almahmoud H, Natale E, Mallmann-Trenn F. Order statistics in population protocols via simple dynamics. In: <i>Proceedings of the Annual ACM Symposium on Principles of Distributed Computing</i>. Association for Computing Machinery; 2026:425-436. doi:<a href=\"https://doi.org/10.1145/3796701.3815922\">10.1145/3796701.3815922</a>","mla":"D’Archivio, Niccolò, et al. “Order Statistics in Population Protocols via Simple Dynamics.” <i>Proceedings of the Annual ACM Symposium on Principles of Distributed Computing</i>, Association for Computing Machinery, 2026, pp. 425–36, doi:<a href=\"https://doi.org/10.1145/3796701.3815922\">10.1145/3796701.3815922</a>.","ieee":"N. D’Archivio, H. Almahmoud, E. Natale, and F. Mallmann-Trenn, “Order statistics in population protocols via simple dynamics,” in <i>Proceedings of the Annual ACM Symposium on Principles of Distributed Computing</i>, Egham, United Kingdom, 2026, pp. 425–436.","chicago":"D’Archivio, Niccolò, Hind Almahmoud, Emanuele Natale, and Frederik Mallmann-Trenn. “Order Statistics in Population Protocols via Simple Dynamics.” In <i>Proceedings of the Annual ACM Symposium on Principles of Distributed Computing</i>, 425–36. Association for Computing Machinery, 2026. <a href=\"https://doi.org/10.1145/3796701.3815922\">https://doi.org/10.1145/3796701.3815922</a>."},"publication_identifier":{"isbn":["9798400725128"]},"_id":"22368","day":"01","OA_place":"publisher","publication_status":"published","ddc":["000"],"has_accepted_license":"1","OA_type":"gold","acknowledgement":"This work has been supported by the AID INRIA-DGA project\r\nn°2023000872 “BioSwarm”, the French government National Research Agency (ANR) through the UCA JEDI (ANR-15-IDEX-01),\r\nthe EUR DS4H (ANR-17-EURE-004) and the 3IA Cote d’Azur Investments ANR-23-IACL-0001, and EPSRC grant EP/W005573/1","scopus_import":"1","corr_author":"1","date_created":"2026-07-19T22:01:47Z","conference":{"end_date":"2026-07-10","location":"Egham, United Kingdom","name":"PODC: Symposium on Principles of Distributed Computing","start_date":"2026-07-06"},"type":"conference","oa_version":"Published Version","publication":"Proceedings of the Annual ACM Symposium on Principles of Distributed Computing","status":"public","language":[{"iso":"eng"}],"month":"07","year":"2026","page":"425-436","oa":1,"publisher":"Association for Computing Machinery","abstract":[{"text":"We study simple dynamics in the population protocol model, in\r\nwhich 𝑛 agents start with totally ordered initial opinions 𝑥1, 𝑥2, . . . ,\r\n𝑥𝑛 and, in each round, a randomly chosen agent changes its opinion\r\nas a function of the opinion of other randomly chosen agents. Such\r\ndynamics often converge to consensus on a single fixation value 𝑋ˆ.\r\nThis paper asks how to control the distribution of 𝑋ˆ as a randomised\r\nchoice among the initial opinions by designing suitable simple\r\ndynamics. Writing the sorted initial values as 𝑥(1) ≤ · · · ≤ 𝑥(𝑛)\r\n,\r\nwe design two protocols that realise natural target laws over order\r\nstatistics.\r\nFirst, for a parameter 𝑝 ∈ (0, 1), our geometric protocol biases\r\ntoward larger opinions and satisfies P\r\n\r\n𝑋ˆ = 𝑥(𝑘)\r\n\r\n∝ 𝑝\r\n𝑛−𝑘\r\n, for\r\n𝑘 = 1, . . . , 𝑛. Equivalently, P\r\n\r\n𝑋ˆ = 𝑥(𝑘)\r\n\r\n= (1 − 𝑝)𝑝\r\n𝑛−𝑘\r\n/(1 − 𝑝\r\n𝑛\r\n).\r\nSecond, our binomial protocol assigns a shifted binomial law to the\r\nranks in ascending order: if 𝐾 −1 ∼ Bin(𝑛−1, 1−𝑝), then 𝑋ˆ = 𝑥(𝐾)\r\n,\r\ni.e., P\r\n\r\n𝑋ˆ = 𝑥(𝑘)\r\n\r\n=\r\n𝑛−1\r\n𝑘−1\r\n\u0001\r\n𝑝\r\n𝑛−𝑘\r\n(1 − 𝑝)\r\n𝑘−1\r\n, for 𝑘 = 1, . . . , 𝑛.\r\nApplications of this include computing the Top-𝑘 values for\r\nsmall 𝑘 on general interaction graphs. A central contribution of\r\nthis work is that, in contrast to most population protocols, we can\r\ncharacterise the fixation distribution in closed form. This is enabled\r\nby a novel analysis technique, which also yields applications: we\r\nderive new results for the Median protocol that extend the state of\r\nthe art.","lang":"eng"}],"article_processing_charge":"No","researchdata_availability":"no","department":[{"_id":"MoHe"}],"supplementarymaterial":"no","author":[{"first_name":"Niccolò","last_name":"D'Archivio","full_name":"D'Archivio, Niccolò"},{"first_name":"Hind","last_name":"Almahmoud","full_name":"Almahmoud, Hind"},{"last_name":"Natale","first_name":"Emanuele","full_name":"Natale, Emanuele"},{"id":"68748c44-84d5-11f1-b4f6-ca083374e553","first_name":"Frederik","last_name":"Mallmann-Trenn","full_name":"Mallmann-Trenn, Frederik"}],"date_published":"2026-07-01T00:00:00Z","title":"Order statistics in population protocols via simple dynamics","date_updated":"2026-07-21T07:34:49Z","das_tickbox":"0","tmp":{"image":"/images/cc_by.png","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"}}]