{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,3]],"date-time":"2026-04-03T04:30:25Z","timestamp":1775190625790,"version":"3.50.1"},"reference-count":20,"publisher":"Association for Computing Machinery (ACM)","issue":"1","license":[{"start":{"date-parts":[[2008,2,1]],"date-time":"2008-02-01T00:00:00Z","timestamp":1201824000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"funder":[{"DOI":"10.13039\/501100001742","name":"United States-Israel Binational Science Foundation","doi-asserted-by":"publisher","award":["95-00238"],"award-info":[{"award-number":["95-00238"]}],"id":[{"id":"10.13039\/501100001742","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["J. ACM"],"published-print":{"date-parts":[[2008,2]]},"abstract":"<jats:p>\n            We consider a failure-free, asynchronous message passing network with\n            <jats:italic>n<\/jats:italic>\n            links, where the processors are arranged on a ring or a chain. The processors are identically programmed but have distinct identities, taken from {0, 1,\u2026 ,\n            <jats:italic>M<\/jats:italic>\n            \u2212 1}. We investigate the communication costs of three well studied tasks: Consensus, Leader, and MaxF (finding the maximum identity). We show that in chain and ring topologies, the message complexities of all three tasks are the same. Hence, we study a finer measure of complexity: the number of transmitted\n            <jats:italic>bits<\/jats:italic>\n            required to solve a task\n            <jats:italic>T<\/jats:italic>\n            , denoted\n            <jats:italic>BitC<\/jats:italic>\n            (\n            <jats:italic>T<\/jats:italic>\n            ).\n          <\/jats:p>\n          <jats:p>\n            We prove several new lower bounds (and some simple upper bounds) that imply the following results: For the two processors case,\n            <jats:italic>BitC<\/jats:italic>\n            (Consensus) = 2 and\n            <jats:italic>BitC<\/jats:italic>\n            (Leader) =\n            <jats:italic>BitC<\/jats:italic>\n            (MaxF) = 2log\n            <jats:sub>2<\/jats:sub>\n            <jats:italic>M<\/jats:italic>\n            \u00b1\n            <jats:italic>O<\/jats:italic>\n            (1), where the gap between the lower and upper bounds is almost always 1. For a chain,\n            <jats:italic>BitC<\/jats:italic>\n            (Consensus) = \u0398(\n            <jats:italic>n<\/jats:italic>\n            ),\n            <jats:italic>BitC<\/jats:italic>\n            (Leader) = \u0398(\n            <jats:italic>n<\/jats:italic>\n            + log\n            <jats:italic>M<\/jats:italic>\n            ), and\n            <jats:italic>BitC<\/jats:italic>\n            (MaxF) = \u0398(\n            <jats:italic>n<\/jats:italic>\n            log\n            <jats:italic>M<\/jats:italic>\n            ). For the ring topology, we prove the lower bound of \u03a9(\n            <jats:italic>n<\/jats:italic>\n            log\n            <jats:italic>M<\/jats:italic>\n            ) for Leader, and (hence) MaxF.\n          <\/jats:p>\n          <jats:p>\n            We consider also a chain where the intermediate processors have no identities. We prove that\n            <jats:italic>BitC<\/jats:italic>\n            (Leader) = \u0398(\n            <jats:italic>n<\/jats:italic>\n            log\n            <jats:italic>M<\/jats:italic>\n            ), which is equal to\n            <jats:italic>n<\/jats:italic>\n            times the bit complexity of the problem for two processors. For the specific case when the chain length is even, we prove that\n            <jats:italic>BitC<\/jats:italic>\n            (Leader) = \u0398(\n            <jats:italic>n<\/jats:italic>\n            ), for both above settings. In addition, we show that for any algorithm solving MaxF, there exists an input, for which\n            <jats:italic>every<\/jats:italic>\n            execution has the bit complexity \u03a9(\n            <jats:italic>n<\/jats:italic>\n            log\n            <jats:italic>M<\/jats:italic>\n            ) (this is not the case for Leader).\n          <\/jats:p>\n          <jats:p>In our proofs, we use both methods of distributed computing and of communication complexity theory, establishing new links between the two areas.<\/jats:p>","DOI":"10.1145\/1326554.1326557","type":"journal-article","created":{"date-parts":[[2008,2,28]],"date-time":"2008-02-28T14:02:33Z","timestamp":1204207353000},"page":"1-28","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":19,"title":["Bit complexity of breaking and achieving symmetry in chains and rings"],"prefix":"10.1145","volume":"55","author":[{"given":"Yefim","family":"Dinitz","sequence":"first","affiliation":[{"name":"Ben-Gurion University of the Negev, Beer-Sheva, Israel"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shlomo","family":"Moran","sequence":"additional","affiliation":[{"name":"The Technion, Haifa, Israel"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Sergio","family":"Rajsbaum","sequence":"additional","affiliation":[{"name":"UNAM, Ciudad Universitaria, M\u00e9xico"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2008,2,22]]},"reference":[{"key":"e_1_2_1_1_1","volume-title":"Distributed Computing: Fundamentals, Simulations and Advanced Topics. McGraw--Hill","author":"Attiya H.","year":"1998","unstructured":"Attiya , H. , and Welch , J . 1998 . Distributed Computing: Fundamentals, Simulations and Advanced Topics. McGraw--Hill , New York . Attiya, H., and Welch, J. 1998. Distributed Computing: Fundamentals, Simulations and Advanced Topics. McGraw--Hill, New York."},{"key":"e_1_2_1_2_1","doi-asserted-by":"publisher","DOI":"10.1016\/0304-3975(91)90193-6"},{"key":"e_1_2_1_3_1","doi-asserted-by":"publisher","DOI":"10.1006\/inco.1994.1002"},{"key":"e_1_2_1_5_1","doi-asserted-by":"publisher","DOI":"10.1145\/258533.258622"},{"key":"e_1_2_1_6_1","doi-asserted-by":"publisher","DOI":"10.1145\/301250.301314"},{"key":"e_1_2_1_7_1","doi-asserted-by":"publisher","DOI":"10.1016\/S1570-8667(03)00024-8"},{"key":"e_1_2_1_8_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.tcs.2007.04.027"},{"key":"e_1_2_1_9_1","doi-asserted-by":"publisher","DOI":"10.1016\/0022-0000(91)90002-M"},{"key":"e_1_2_1_10_1","doi-asserted-by":"publisher","DOI":"10.1145\/872035.872066"},{"key":"e_1_2_1_11_1","doi-asserted-by":"publisher","DOI":"10.1145\/357195.357200"},{"key":"e_1_2_1_12_1","doi-asserted-by":"publisher","DOI":"10.1145\/359024.359029"},{"key":"e_1_2_1_13_1","doi-asserted-by":"publisher","DOI":"10.1145\/800222.806747"},{"key":"e_1_2_1_14_1","doi-asserted-by":"crossref","unstructured":"Kushilevitz E. and Nisan N. 1997. Communication Complexity. Cambridge University Press Cambridge UK.   Kushilevitz E. and Nisan N. 1997. Communication Complexity. Cambridge University Press Cambridge UK.","DOI":"10.1017\/CBO9780511574948"},{"key":"e_1_2_1_15_1","doi-asserted-by":"publisher","DOI":"10.1007\/s004930050054"},{"key":"e_1_2_1_16_1","volume-title":"Distributed Algorithms. Morgan-Kaufmann","author":"Lynch N. A.","unstructured":"Lynch , N. A. 1996. Distributed Algorithms. Morgan-Kaufmann . San Francisco, CA . Lynch, N. A. 1996. Distributed Algorithms. Morgan-Kaufmann. San Francisco, CA."},{"key":"e_1_2_1_17_1","doi-asserted-by":"publisher","DOI":"10.1137\/0222028"},{"key":"e_1_2_1_18_1","doi-asserted-by":"publisher","DOI":"10.1016\/0020-0190(87)90052-4"},{"key":"e_1_2_1_19_1","volume-title":"Introduction to Distributed Algorithms","author":"Tel G.","unstructured":"Tel , G. 1994. Introduction to Distributed Algorithms , Cambridge University Press , Cambridge, UK . Tel, G. 1994. Introduction to Distributed Algorithms, Cambridge University Press, Cambridge, UK."},{"key":"e_1_2_1_20_1","doi-asserted-by":"publisher","DOI":"10.1145\/31846.32978"},{"key":"e_1_2_1_21_1","doi-asserted-by":"publisher","DOI":"10.1145\/800135.804414"}],"container-title":["Journal of the ACM"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/1326554.1326557","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/1326554.1326557","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T13:56:25Z","timestamp":1750254985000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/1326554.1326557"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2008,2]]},"references-count":20,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2008,2]]}},"alternative-id":["10.1145\/1326554.1326557"],"URL":"https:\/\/doi.org\/10.1145\/1326554.1326557","relation":{},"ISSN":["0004-5411","1557-735X"],"issn-type":[{"value":"0004-5411","type":"print"},{"value":"1557-735X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2008,2]]},"assertion":[{"value":"2004-08-01","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2007-10-01","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2008-02-22","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}