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Discrete Math."],"published-print":{"date-parts":[[2018,1]]},"abstract":"<jats:p>We consider an asynchronous voting process on graphs called discordant voting, which can be described as follows. Initially each vertex holds one of two opinions, red or blue. Neighboring vertices with different opinions interact pairwise along an edge. After an interaction both vertices have the same color. The quantity of interest is the time to reach consensus, i.e., the number of steps needed for all vertices have the same color. We show that for a given initial coloring of the vertices, the expected time to reach consensus depends strongly on the underlying graph and the update rule (i.e., push, pull, oblivious).<\/jats:p>","DOI":"10.1137\/16m1105979","type":"journal-article","created":{"date-parts":[[2018,10,16]],"date-time":"2018-10-16T15:11:30Z","timestamp":1539702690000},"page":"2398-2420","source":"Crossref","is-referenced-by-count":3,"title":["Discordant Voting Processes on Finite Graphs"],"prefix":"10.1137","volume":"32","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5264-4401","authenticated-orcid":true,"given":"Colin","family":"Cooper","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2018-0374","authenticated-orcid":true,"given":"Martin","family":"Dyer","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Alan","family":"Frieze","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Nicol\u00e1s","family":"Rivera","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2018,10,16]]},"reference":[{"key":"atypb2","unstructured":"A. Basak, R. Durrett, and Y. Zhang,\n                      The Evolving Voter Model on Thick Graphs\n                      , preprint,https:\/\/arxiv.org\/abs\/1512.07871, 2015."},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1214\/16-AAP1230"},{"key":"atypb4","unstructured":"P. Berenbrink, G. Giakkoupis, A. Kermarrec, and F. Mallmann-Trenn,\n                      Bounds on the Voter Model in Dynamic Networks\n                      , preprint,https:\/\/arxiv.org\/abs\/1603.01895, 2016."},{"key":"atypb5","doi-asserted-by":"publisher","DOI":"10.1137\/080729542"},{"key":"atypb6","doi-asserted-by":"publisher","DOI":"10.1137\/120900368"},{"key":"atypb7","unstructured":"C. Cooper and N. Rivera,\n                      The linear voting model\n                      , in Proceedings of the 43rd International Colloquium on Automata, Languages, and Programming (ICALP), 2016, pp. 144:1-144:12."},{"key":"atypb8","doi-asserted-by":"publisher","DOI":"10.1214\/aop\/1176991158"},{"key":"atypb9","doi-asserted-by":"publisher","DOI":"10.1007\/BF01580137"},{"key":"atypb10","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.1200709109"},{"key":"atypb11","unstructured":"W. Feller,\n                      An Introduction to Probability Theory and Its Applications\n                      , Vol. 1, 3rd ed., Wiley, New York, 1968."},{"key":"atypb12","doi-asserted-by":"crossref","unstructured":"T. Gross and H. Sayama, eds.\n                      Adaptive Networks Theory, Models and Applications\n                      , Springer, New York, 2009.","DOI":"10.1007\/978-3-642-01284-6"},{"key":"atypb13","doi-asserted-by":"publisher","DOI":"10.1006\/inco.2001.3088"},{"key":"atypb14","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.74.056108"},{"key":"atypb15","doi-asserted-by":"crossref","unstructured":"D. Levin, Y. Peres, and E. Wilmer, Markov Chains and Mixing Times, AMS, Providence, RI, 2009.","DOI":"10.1090\/mbk\/058"},{"key":"atypb16","doi-asserted-by":"crossref","unstructured":"T. Liggett,\n                      Stochastic Interacting Systems: Contact, Voter and Exclusion Processes\n                      , Springer, New York, 1999.","DOI":"10.1007\/978-3-662-03990-8"},{"key":"atypb17","doi-asserted-by":"publisher","DOI":"10.1007\/s10994-006-9713-5"},{"key":"atypb18","first-page":"330","author":"Nakata T.","year":"1999","journal-title":"Proceedings of COCOON"},{"key":"atypb19","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-2011-05523-6"},{"key":"atypb20","unstructured":"A. Pongr\u00e1cz,\n                      Discordant voting protocols for cyclically linked agents\n                      , Proceedings of the World Congress on Engineering, Vol. I, London, 2018."},{"key":"atypb21","doi-asserted-by":"publisher","DOI":"10.1016\/j.camwa.2012.12.005"},{"key":"atypb22","doi-asserted-by":"publisher","DOI":"10.1006\/eujc.1993.1038"},{"key":"atypb23","doi-asserted-by":"crossref","unstructured":"D. Williams,\n                      Probability with Martingales\n                      , Cambridge University Press, Cambridge, 1991.","DOI":"10.1017\/CBO9780511813658"}],"container-title":["SIAM Journal on Discrete Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/16M1105979","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T12:53:40Z","timestamp":1787316820000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/16M1105979"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,1]]},"references-count":22,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2018,1]]}},"alternative-id":["10.1137\/16M1105979"],"URL":"https:\/\/doi.org\/10.1137\/16m1105979","relation":{},"ISSN":["0895-4801","1095-7146"],"issn-type":[{"value":"0895-4801","type":"print"},{"value":"1095-7146","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,1]]}}}