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ACM"],"published-print":{"date-parts":[[2012,2]]},"abstract":"<jats:p>\n            In the\n            <jats:italic>renaming<\/jats:italic>\n            task,\n            <jats:italic>n<\/jats:italic>\n            +1 processes start with unique input names from a large space and must choose unique output names taken from a smaller name space, 0,1,\u2026,\n            <jats:italic>K<\/jats:italic>\n            . To rule out trivial solutions, a protocol must be\n            <jats:italic>anonymous<\/jats:italic>\n            : the value chosen by a process can depend on its input name and on the execution, but not on the specific process ID.\n          <\/jats:p>\n          <jats:p>\n            Attiya et al. [1990] showed that renaming has a wait-free solution when\n            <jats:italic>K<\/jats:italic>\n            \u2265 2\n            <jats:italic>n<\/jats:italic>\n            . Several algebraic topology proofs of a lower bound stating that no such protocol exists when\n            <jats:italic>K<\/jats:italic>\n            &lt; 2\n            <jats:italic>n<\/jats:italic>\n            have been published. In a companion article, we present the first completely combinatorial renaming lower bound proof stating if\n            <jats:italic>n<\/jats:italic>\n            + 1 is a primer power, then renaming is not wait-free solvable when\n            <jats:italic>K<\/jats:italic>\n            &lt; 2\n            <jats:italic>n<\/jats:italic>\n            . In this article, we show that if\n            <jats:italic>n<\/jats:italic>\n            + 1 is not a primer power, then there exists a wait-free renaming protocol for\n            <jats:italic>K<\/jats:italic>\n            = 2\n            <jats:italic>n<\/jats:italic>\n            \u22121. Therefore the renaming lower bound for\n            <jats:italic>K<\/jats:italic>\n            &lt; 2\n            <jats:italic>n<\/jats:italic>\n            is incorrect. More precisely, our main theorem states that there exists a wait-free renaming protocol for\n            <jats:italic>K<\/jats:italic>\n            &lt; 2\n            <jats:italic>n<\/jats:italic>\n            if and only if\n            <jats:italic>n<\/jats:italic>\n            + 1 is not a prime power. We prove this result using the known equivalence of\n            <jats:italic>K<\/jats:italic>\n            -renaming for\n            <jats:italic>K<\/jats:italic>\n            = 2\n            <jats:italic>n<\/jats:italic>\n            \u2212 1 and the\n            <jats:italic>weak symmetry breaking<\/jats:italic>\n            task: processes have no input values and the output values are 0 or 1, and it is required that in every execution in which all processes participate, at least one process decides 1 and at least one process decides 0.\n          <\/jats:p>","DOI":"10.1145\/2108242.2108245","type":"journal-article","created":{"date-parts":[[2012,2,28]],"date-time":"2012-02-28T12:58:35Z","timestamp":1330433915000},"page":"1-49","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":34,"title":["New combinatorial topology bounds for renaming"],"prefix":"10.1145","volume":"59","author":[{"given":"Armando","family":"Casta\u00f1eda","sequence":"first","affiliation":[{"name":"Universidad Nacional Aut\u00f3noma de M\u00e9xico, M\u00e9xico"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Sergio","family":"Rajsbaum","sequence":"additional","affiliation":[{"name":"Universidad Nacional Aut\u00f3noma de M\u00e9xico, M\u00e9xico"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2012,3,2]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"publisher","DOI":"10.1145\/200836.200869"},{"key":"e_1_2_1_2_1","doi-asserted-by":"publisher","DOI":"10.1145\/79147.79158"},{"key":"e_1_2_1_3_1","doi-asserted-by":"publisher","DOI":"10.1137\/S0097539797330689"},{"key":"e_1_2_1_4_1","volume-title":"Distributed Computing: Fundamentals, Simulations and Advanced Topics","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_5_1","doi-asserted-by":"publisher","DOI":"10.1145\/167088.167119"},{"key":"e_1_2_1_6_1","doi-asserted-by":"publisher","DOI":"10.1145\/164051.164056"},{"key":"e_1_2_1_7_1","doi-asserted-by":"publisher","DOI":"10.1145\/259380.259439"},{"key":"e_1_2_1_8_1","unstructured":"Casta\u00f1eda A. Herlihy M. and Rajsbaum S. 2011. An equivariance theorem with applications to renaming. Tech rep. &num;1975 IRISA Universit\u00e9 de Rennes 1 (France) http:\/\/hal.inria.fr\/docs\/00\/58\/61\/90\/PDF\/PI-1975.pdf.  Casta\u00f1eda A. Herlihy M. and Rajsbaum S. 2011. An equivariance theorem with applications to renaming. 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