[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-83367-en":3,"doc-seo-83367-105":29,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":13,"seo_description":14,"update_tm":27,"read_time":28},83367,1099514068365,"Aurelia","https://ap-avatar.wpscdn.com/avatar/10000253d8d9f28188e?_k=1776742907772140068",8,"Research & Report","Computing in Anonymous Dynamic Networks with One-Bit Communications","This paper studies deterministic computation in anonymous dynamic networks where each agent broadcasts a single bit per round and only learns neighbor counts for each bit value. Despite this minimal bandwidth, it shows that nontrivial global computation remains feasible. With a unique leader and a known size upper bound U, it provides a terminating algorithm for any computable function of the input multiset in O(n^3 log^2 n + U) rounds. Without prior knowledge of n, a stabilizing algorithm achieves O(n^3 log^2 n).","arXiv :2607 .08358v2 [ cs .DC] 11 Jul 2026  \nComputing in Anonymous Dynamic Networks with One-Bit  \nCommunications  \nThibaut Blanc (ENS de Lyon)  \n[thibaut. blanc@ens-lyon. fr](thibaut. blanc@ens-lyon. fr)  \nGiuseppe Antonio Di Luna (Sapienza University of Rome) [diluna@diag. uniroma1. it](diluna@diag. uniroma1. it)  \nGiovanni Viglietta (University of Aizu)  \n[viglietta@gmail. com](viglietta@gmail. com)  \nAbstract  \nWe initiate the study of deterministic computation in anonymous dynamic networks in which each agent broadcasts a single bit per round and receives only the number of neighbors that broadcast each bit value. Despite this minimal communication, we show that surprisingly rich global computation remains possible.  \nWhen the network has a unique leader and an upper bound U on the network size n is known, we give a terminating algorithm for any desired computable function of the input multiset in O (n3 log2 n + U) rounds, where inputs are drawn from a universe of size N = 2O (nlog n) . In addition, without any prior knowledge of n, we design a stabilizing algorithm for the same task that runs in O(n3 log2 n) rounds. Notably, this essentially matches the state of the art for the congested communication model, where messages may carry O (log n) bits rather than just one, and general computation is achieved in O (n3 ) rounds. We also obtain companion results for leaderless and multi-leader networks, with comparable performance.  \nWe complement these upper bounds with an almost-matching lower bound of  \nΩ 􀀒 n2~~ ~~lolgog(Nn/n) 􀀓  \nrounds, which becomes Ω(n3 ) when N = 2Ω(nlog n) . The proof is an information-theoretic argument on local histories, and the lower bound holds even when the network has a unique leader, n and N are known, and the communication graph is restricted to a ring that may change every round.  \nOur algorithmic techniques are based on extracting global linear equations from local one-bit aggregate observations. A one-bit cut test gives a conservation constraint on the sizes of indistinguishable agent classes; by repeatedly refining these classes and collecting independent constraints, the agents recover the desired multiplicities. For the unknown-size case, we also introduce a self-correcting adaptive flooding primitive of independent interest. Together, these results show that the computational power of congested anonymous dynamic networks is essentially preserved, even when every message is compressed to a single bit.  \n1 Introduction  \nDynamic networks are a central research topic in distributed computing. In these systems, communication links may change unpredictably over time. One of the most widely studied models is the 1-interval-connected model. In this synchronous model, a system of n agents proceeds in roundsand, in every round t, an adversary selects an arbitrary communication graph Gt subject only to the requirement that Gt be connected.  \nIn this paper, we focus on anonymous dynamic networks. Agents do not have unique identifiersand execute the same deterministic algorithm. Except for their input, agents start in the same state. Anonymous networks arise naturally when identifiers are unavailable, undesirable, or incompatible with the application, for example in privacy-sensitive systems, large-scale populations of simple devices, and biological systems in which globally unique identifiers do not exist. From an algorithmic perspective, however, anonymity creates a fundamental symmetry problem: agents with identical local histories must remain in identical states.  \nIt is often customary to make the minimal symmetry-breaking assumption that the network contains a set of leader agents, namely a set of agents with a distinguished initial state whose exact size k is known. The assumption of having a unique leader is the special case in which k = 1 . Asymmetry-breaking assumption is generally necessary [31] for distributed algorithms computing functions that depend on the absolute scale of the syst","cbCaisKnQTvjidqp","https://ap.wps.com/l/cbCaisKnQTvjidqp","pdf",622177,1,46,"English","en",105,"# Abstract\n# Introduction\n## Contributions\n## Quadratic lower bound","[{\"question\":\"What is the one-bit communication model used in this work?\",\"answer\":\"In each round, every agent broadcasts exactly one bit to its current neighbors. Each agent receives only the number of neighbors that broadcast 0 and the number that broadcast 1 in that round.\"},{\"question\":\"How do the authors compute functions of the input multiset?\",\"answer\":\"They provide algorithms that recover desired multiplicities of input values using global linear equations derived from local one-bit aggregate observations. A one-bit cut test yields conservation constraints, which are refined and solved to obtain the correct multiplicities.\"},{\"question\":\"What performance guarantees are established for cases with and without knowledge of n?\",\"answer\":\"With a unique leader and a known upper bound U on n, the paper gives a terminating algorithm running in O(n^3 log^2 n + U) rounds. Without prior knowledge of n, it designs a stabilizing algorithm for the same task in O(n^3 log^2 n) rounds, matching prior best results up to logarithmic factors.\"}]",1784187025,116,{"code":4,"msg":30,"data":31},"ok",{"site_id":24,"language":23,"slug":32,"title":13,"keywords":33,"description":14,"schema_data":34,"social_meta":86,"head_meta":88,"extra_data":90,"updated_unix":27},"computing-in-anonymous-dynamic-networks-with-one-bit-communications","",{"@graph":35,"@context":85},[36,53,68],{"@type":37,"itemListElement":38},"BreadcrumbList",[39,43,47,50],{"item":40,"name":41,"@type":42,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":44,"name":45,"@type":42,"position":46},"https://docshare.wps.com/document/","Document",2,{"item":48,"name":12,"@type":42,"position":49},"https://docshare.wps.com/document/research-report/",3,{"item":51,"name":13,"@type":42,"position":52},"https://docshare.wps.com/document/computing-in-anonymous-dynamic-networks-with-one-bit-communications/83367/",4,{"url":51,"name":13,"@type":54,"author":55,"headline":13,"publisher":57,"fileFormat":60,"inLanguage":23,"description":14,"dateModified":61,"datePublished":62,"encodingFormat":60,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":56},"Person",{"url":40,"name":58,"@type":59},"DocShare","Organization","application/pdf","2026-07-21","2026-07-16",true,{"@type":65,"interactionType":66,"userInteractionCount":20},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"What is the one-bit communication model used in this work?","Question",{"text":75,"@type":76},"In each round, every agent broadcasts exactly one bit to its current neighbors. Each agent receives only the number of neighbors that broadcast 0 and the number that broadcast 1 in that round.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How do the authors compute functions of the input multiset?",{"text":80,"@type":76},"They provide algorithms that recover desired multiplicities of input values using global linear equations derived from local one-bit aggregate observations. A one-bit cut test yields conservation constraints, which are refined and solved to obtain the correct multiplicities.",{"name":82,"@type":73,"acceptedAnswer":83},"What performance guarantees are established for cases with and without knowledge of n?",{"text":84,"@type":76},"With a unique leader and a known upper bound U on n, the paper gives a terminating algorithm running in O(n^3 log^2 n + U) rounds. 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