{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,29]],"date-time":"2025-09-29T08:10:08Z","timestamp":1759133408792,"version":"3.41.0"},"reference-count":50,"publisher":"Association for Computing Machinery (ACM)","issue":"1","license":[{"start":{"date-parts":[[2019,11,15]],"date-time":"2019-11-15T00:00:00Z","timestamp":1573776000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"funder":[{"name":"US-Israel Binational Science Foundation","award":["2016419"],"award-info":[{"award-number":["2016419"]}]},{"name":"European Research Council"},{"DOI":"10.13039\/100000001","name":"NSF","doi-asserted-by":"publisher","award":["CCF-1527867, CCF-1540512, IIS-1633720, and CCF-1717075"],"award-info":[{"award-number":["CCF-1527867, CCF-1540512, IIS-1633720, and CCF-1717075"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"name":"European Union's Horizon 2020 research and innovation programme","award":["715672"],"award-info":[{"award-number":["715672"]}]}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Algorithms"],"published-print":{"date-parts":[[2020,1,31]]},"abstract":"<jats:p>\n            This article presents a randomized (Las Vegas) distributed algorithm that constructs a minimum spanning tree (MST) in weighted networks with optimal (up to polylogarithmic factors) time and message complexity. This algorithm runs in \u00d5(\n            <jats:italic>D<\/jats:italic>\n            + \u221a\n            <jats:italic>n<\/jats:italic>\n            ) time and exchanges \u00d5(\n            <jats:italic>m<\/jats:italic>\n            ) messages (both with high probability), where\n            <jats:italic>n<\/jats:italic>\n            is the number of nodes of the network,\n            <jats:italic>D<\/jats:italic>\n            is the hop-diameter, and\n            <jats:italic>m<\/jats:italic>\n            is the number of edges. This is the\n            <jats:italic>first<\/jats:italic>\n            distributed MST algorithm that matches\n            <jats:italic>simultaneously<\/jats:italic>\n            the time lower bound of \u03a9\n            <jats:sup>\u02dc<\/jats:sup>\n            (\n            <jats:italic>D<\/jats:italic>\n            + \u221a\n            <jats:italic>n<\/jats:italic>\n            ) [10] and the message lower bound of \u03a9 (\n            <jats:italic>m<\/jats:italic>\n            ) [31], which both apply to randomized Monte Carlo algorithms.\n          <\/jats:p>\n          <jats:p>\n            The prior time and message lower bounds are derived using two completely different graph constructions; the existing lower-bound construction that shows one lower bound does not work for the other. To complement our algorithm, we present a new lower-bound graph construction for which any distributed MST algorithm requires both \u03a9\n            <jats:sup>\u02dc<\/jats:sup>\n            (\n            <jats:italic>D<\/jats:italic>\n            + \u221a\n            <jats:italic>n<\/jats:italic>\n            ) rounds and \u03a9 (\n            <jats:italic>m<\/jats:italic>\n            ) messages.\n          <\/jats:p>","DOI":"10.1145\/3365005","type":"journal-article","created":{"date-parts":[[2019,11,15]],"date-time":"2019-11-15T21:16:57Z","timestamp":1573852617000},"page":"1-27","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":3,"title":["A Time- and Message-Optimal Distributed Algorithm for Minimum Spanning Trees"],"prefix":"10.1145","volume":"16","author":[{"given":"Gopal","family":"Pandurangan","sequence":"first","affiliation":[{"name":"University of Houston, Houston, TX, USA"}]},{"given":"Peter","family":"Robinson","sequence":"additional","affiliation":[{"name":"City University of Hong Kong, Kowloon, Hong Kong"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9108-2448","authenticated-orcid":false,"given":"Michele","family":"Scquizzato","sequence":"additional","affiliation":[{"name":"University of Padova, Padova, Italy"}]}],"member":"320","published-online":{"date-parts":[[2019,11,15]]},"reference":[{"volume-title":"Distributed Computing: Fundamentals, Simulations and Advanced Topics","year":"1998","author":"Attiya Hagit","key":"e_1_2_1_1_1"},{"key":"e_1_2_1_2_1","doi-asserted-by":"publisher","DOI":"10.1145\/28395.28421"},{"key":"e_1_2_1_3_1","doi-asserted-by":"publisher","DOI":"10.1145\/77600.77618"},{"key":"e_1_2_1_4_1","doi-asserted-by":"publisher","DOI":"10.1109\/FSCS.1990.89571"},{"volume-title":"Proceedings of the 26th IEEE Symposium on Foundations of Computer Science (FOCS). 257--266","author":"Chin Francis","key":"e_1_2_1_5_1"},{"key":"e_1_2_1_6_1","doi-asserted-by":"publisher","DOI":"10.1145\/12130.12151"},{"key":"e_1_2_1_7_1","doi-asserted-by":"publisher","DOI":"10.1137\/11085178X"},{"key":"e_1_2_1_8_1","article-title":"Distributed random walks","volume":"60","author":"Sarma Atish Das","year":"2013","journal-title":"J. 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