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Algorithms"],"published-print":{"date-parts":[[2014,10,28]]},"abstract":"<jats:p>\n            A team consisting of an unknown number of mobile agents, starting from different nodes of an unknown network, have to meet at the same node. Agents move in synchronous rounds. Each agent has a different label. Up to\n            <jats:italic>f<\/jats:italic>\n            of the agents are Byzantine. We consider two levels of Byzantine behavior. A strongly Byzantine agent can choose an arbitrary port when it moves and it can convey arbitrary information to other agents, while a weakly Byzantine agent can do the same, except changing its label. What is the minimum number of good agents that guarantees deterministic gathering of all of them, with termination? We solve exactly this Byzantine gathering problem in arbitrary networks for weakly Byzantine agents and give approximate solutions for strongly Byzantine agents, both when the size of the network is known and when it is unknown. It turns out that both the strength versus the weakness of Byzantine behavior and the knowledge of network size significantly impact the results.\n          <\/jats:p>\n          <jats:p>\n            For weakly Byzantine agents, we show that any number of good agents permits solving the problem for networks of known size. If the size is unknown, then this minimum number is\n            <jats:italic>f<\/jats:italic>\n            +2. More precisely, we show a deterministic polynomial algorithm that gathers all good agents in an arbitrary network, provided that there are at least\n            <jats:italic>f<\/jats:italic>\n            +2 of them. We also provide a matching lower bound: we prove that if the number of good agents is at most\n            <jats:italic>f<\/jats:italic>\n            +1, then they are not able to gather deterministically with termination in some networks.\n          <\/jats:p>\n          <jats:p>\n            For strongly Byzantine agents, we give a lower bound of\n            <jats:italic>f<\/jats:italic>\n            +1, even when the graph is known: we show that\n            <jats:italic>f<\/jats:italic>\n            good agents cannot gather deterministically in the presence of\n            <jats:italic>f<\/jats:italic>\n            Byzantine agents even in a ring of known size. On the positive side, we give deterministic gathering algorithms for at least 2\n            <jats:italic>f<\/jats:italic>\n            +1 good agents when the size of the network is known and for at least 4\n            <jats:italic>f<\/jats:italic>\n            +2 good agents when it is unknown.\n          <\/jats:p>","DOI":"10.1145\/2629656","type":"journal-article","created":{"date-parts":[[2014,8,12]],"date-time":"2014-08-12T13:53:48Z","timestamp":1407851628000},"page":"1-28","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":53,"title":["Gathering Despite Mischief"],"prefix":"10.1145","volume":"11","author":[{"given":"Yoann","family":"Dieudonn\u00e9","sequence":"first","affiliation":[{"name":"Universit\u00e9 de Picardie Jules Verne, Amiens, France"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Andrzej","family":"Pelc","sequence":"additional","affiliation":[{"name":"Universit\u00e9 du Qu\u00e9bec en Outaouais, Canada"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"David","family":"Peleg","sequence":"additional","affiliation":[{"name":"Weizmann Institute of Science, Israel"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"320","published-online":{"date-parts":[[2014,8,11]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"publisher","DOI":"10.1137\/050645221"},{"key":"e_1_2_1_2_1","doi-asserted-by":"publisher","DOI":"10.1137\/S0363012993249195"},{"key":"e_1_2_1_3_1","doi-asserted-by":"publisher","DOI":"10.1002\/nav.10011"},{"key":"e_1_2_1_4_1","unstructured":"S. Alpern and S. Gal. 2002. The Theory of Search Games and Rendezvous International Series in Operations research and Management Science number 55. Kluwer Academic.  S. Alpern and S. Gal. 2002. The Theory of Search Games and Rendezvous International Series in Operations research and Management Science number 55. Kluwer Academic."},{"key":"e_1_2_1_5_1","doi-asserted-by":"publisher","DOI":"10.1239\/jap\/1032374243"},{"key":"e_1_2_1_6_1","doi-asserted-by":"publisher","DOI":"10.2307\/3214827"},{"key":"e_1_2_1_7_1","doi-asserted-by":"publisher","DOI":"10.1145\/276884.276925"},{"key":"e_1_2_1_8_1","doi-asserted-by":"publisher","DOI":"10.1287\/opre.49.1.107.11191"},{"key":"e_1_2_1_9_1","doi-asserted-by":"publisher","DOI":"10.1137\/S0363012996314130"},{"key":"e_1_2_1_10_1","doi-asserted-by":"publisher","DOI":"10.1002\/nav.1044"},{"key":"e_1_2_1_11_1","volume-title":"Proceedings of the 14th International Conference on Principles of Distributed Systems (OPODIS\u201910)","author":"Chalopin J.","unstructured":"J. Chalopin , S. Das , and A. Kosowski . 2010. Constructing a map of an anonymous graph: Applications of universal sequences . In Proceedings of the 14th International Conference on Principles of Distributed Systems (OPODIS\u201910) . 119--134. J. Chalopin, S. Das, and A. Kosowski. 2010. Constructing a map of an anonymous graph: Applications of universal sequences. In Proceedings of the 14th International Conference on Principles of Distributed Systems (OPODIS\u201910). 119--134."},{"issue":"2012","key":"e_1_2_1_12_1","first-page":"829","article-title":"Distributed computing by mobile robots","volume":"41","author":"Cieliebak M.","year":"2003","unstructured":"M. Cieliebak , P. Flocchini , G. Prencipe , and N. Santoro . 2003 . Distributed computing by mobile robots : Gathering. SIAM Journal on Computiing 41 ( 2012 ), 829 -- 879 . M. Cieliebak, P. Flocchini, G. Prencipe, and N. Santoro. 2003. Distributed computing by mobile robots: Gathering. SIAM Journal on Computiing 41 (2012), 829--879.","journal-title":"Gathering. 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Kranakis , D. Krizanc , and P. Morin . 2008. Randomized rendez-vous with limited memory . In Proceedings of the 8th Latin American Theoretical Informatics (LATIN\u201908) . Springer, 605--616. E. Kranakis, D. Krizanc, and P. Morin. 2008. Randomized rendez-vous with limited memory. In Proceedings of the 8th Latin American Theoretical Informatics (LATIN\u201908). Springer, 605--616."},{"key":"e_1_2_1_29_1","volume-title":"Proceedings of the 23rd International Conference on Distributed Computing Systems (ICDCS\u201903)","author":"Kranakis E.","unstructured":"E. Kranakis , D. Krizanc , N. Santoro , and C. Sawchuk . 2003. Mobile agent rendezvous in a ring . In Proceedings of the 23rd International Conference on Distributed Computing Systems (ICDCS\u201903) . 592--599. E. Kranakis, D. Krizanc, N. Santoro, and C. Sawchuk. 2003. Mobile agent rendezvous in a ring. In Proceedings of the 23rd International Conference on Distributed Computing Systems (ICDCS\u201903). 592--599."},{"key":"e_1_2_1_30_1","doi-asserted-by":"publisher","DOI":"10.1145\/2332432.2332492"},{"key":"e_1_2_1_31_1","doi-asserted-by":"publisher","DOI":"10.1137\/S036301299427816X"},{"key":"e_1_2_1_32_1","doi-asserted-by":"crossref","unstructured":"M. Mitzenmacher and E. Upfal. 2005. Probability and Computing: Randomized Algorithms and Probabilistic Analysis. Cambridge University Press.   M. Mitzenmacher and E. Upfal. 2005. Probability and Computing: Randomized Algorithms and Probabilistic Analysis. Cambridge University Press.","DOI":"10.1017\/CBO9780511813603"},{"key":"e_1_2_1_33_1","doi-asserted-by":"publisher","DOI":"10.1145\/322186.322188"},{"issue":"2006","key":"e_1_2_1_34_1","first-page":"93","article-title":"Voting mechanisms in asynchronous Byzantine environments","volume":"16","author":"Pelc A.","year":"2012","unstructured":"A. Pelc . 2012 . 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In Proceedings of the International Colloquium on Automata, Languages, and Programming (ICALP\u201996). 610--621."}],"container-title":["ACM Transactions on Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/2629656","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/2629656","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T06:13:30Z","timestamp":1750227210000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/2629656"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,8,11]]},"references-count":43,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2014,10,28]]}},"alternative-id":["10.1145\/2629656"],"URL":"https:\/\/doi.org\/10.1145\/2629656","relation":{},"ISSN":["1549-6325","1549-6333"],"issn-type":[{"value":"1549-6325","type":"print"},{"value":"1549-6333","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,8,11]]},"assertion":[{"value":"2012-01-01","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2014-01-01","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2014-08-11","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}