{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T04:23:58Z","timestamp":1750220638169,"version":"3.41.0"},"reference-count":25,"publisher":"Association for Computing Machinery (ACM)","issue":"4","license":[{"start":{"date-parts":[[2020,11,25]],"date-time":"2020-11-25T00:00:00Z","timestamp":1606262400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"funder":[{"name":"HSE University Basic Research Program"},{"name":"NSF CAREER award","award":["CCF-1149018"],"award-info":[{"award-number":["CCF-1149018"]}]},{"DOI":"10.13039\/100000879","name":"Alfred P. Sloan Foundation","doi-asserted-by":"crossref","award":["Research Fellowship"],"award-info":[{"award-number":["Research Fellowship"]}],"id":[{"id":"10.13039\/100000879","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Comput. Theory"],"published-print":{"date-parts":[[2020,12,31]]},"abstract":"<jats:p>\n            A major goal in complexity theory is to understand the communication complexity of number-on-the-forehead problems\n            <jats:italic>f<\/jats:italic>\n            :({0, 1}\n            <jats:italic>\n              <jats:sup>n<\/jats:sup>\n            <\/jats:italic>\n            )\n            <jats:italic>\n              <jats:sup>k<\/jats:sup>\n            <\/jats:italic>\n            \u2192 {0, 1} with\n            <jats:italic>k<\/jats:italic>\n            &gt; log\n            <jats:italic>n<\/jats:italic>\n            parties. We study the problems of inner product and set disjointness and determine their randomized communication complexity for every\n            <jats:italic>k<\/jats:italic>\n            \u2265 log\n            <jats:italic>n<\/jats:italic>\n            , showing in both cases that \u0398(1 + \u2308log\n            <jats:italic>n<\/jats:italic>\n            \u2309\/ log \u23081 +\n            <jats:italic>k<\/jats:italic>\n            \/ log\n            <jats:italic>n<\/jats:italic>\n            \u2309) bits are necessary and sufficient. In particular, these problems admit constant-cost protocols if and only if the number of parties is\n            <jats:italic>k<\/jats:italic>\n            \u2265\n            <jats:italic>n<\/jats:italic>\n            <jats:sup>\u03f5<\/jats:sup>\n            for some constant \u03f5 &gt; 0.\n          <\/jats:p>","DOI":"10.1145\/3428671","type":"journal-article","created":{"date-parts":[[2020,11,26]],"date-time":"2020-11-26T19:40:43Z","timestamp":1606419643000},"page":"1-28","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":0,"title":["Inner Product and Set Disjointness"],"prefix":"10.1145","volume":"12","author":[{"given":"Vladimir V.","family":"Podolskii","sequence":"first","affiliation":[{"name":"Steklov Mathematical Institute and Higher School of Economics, Pokrovsky Bulvar, Moscow, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Alexander A.","family":"Sherstov","sequence":"additional","affiliation":[{"name":"University of California, Los Angeles, Los Angeles, CA, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2020,11,25]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00037-013-0078-4"},{"key":"e_1_2_1_2_1","doi-asserted-by":"publisher","DOI":"10.1137\/S0097539700375944"},{"key":"e_1_2_1_3_1","doi-asserted-by":"publisher","DOI":"10.1016\/0022-0000(92)90047-M"},{"key":"e_1_2_1_4_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcss.2003.11.006"},{"key":"e_1_2_1_5_1","doi-asserted-by":"publisher","DOI":"10.1137\/100792779"},{"key":"e_1_2_1_6_1","doi-asserted-by":"publisher","DOI":"10.5555\/1328865.1328873"},{"key":"e_1_2_1_7_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00037-007-0220-2"},{"volume-title":"Proceedings of the 15th Annual ACM Symposium on Theory of Computing (STOC\u201983)","author":"Chandra Ashok K.","key":"e_1_2_1_8_1","unstructured":"Ashok K. Chandra , Merrick L. Furst , and Richard J. Lipton . 1983. Multi-party protocols . In Proceedings of the 15th Annual ACM Symposium on Theory of Computing (STOC\u201983) . 94--99. DOI:https:\/\/doi.org\/10.1145\/800061.808737 10.1145\/800061.808737 Ashok K. Chandra, Merrick L. Furst, and Richard J. Lipton. 1983. Multi-party protocols. In Proceedings of the 15th Annual ACM Symposium on Theory of Computing (STOC\u201983). 94--99. DOI:https:\/\/doi.org\/10.1145\/800061.808737"},{"key":"e_1_2_1_9_1","volume-title":"Proceedings of the Electronic Colloquium on Computational Complexity (ECCC\u201908)","author":"Chattopadhyay Arkadev","year":"2008","unstructured":"Arkadev Chattopadhyay and Anil Ada . 2008 . Multiparty communication complexity of disjointness . In Proceedings of the Electronic Colloquium on Computational Complexity (ECCC\u201908) . Report TR08-002. Arkadev Chattopadhyay and Anil Ada. 2008. Multiparty communication complexity of disjointness. In Proceedings of the Electronic Colloquium on Computational Complexity (ECCC\u201908). Report TR08-002."},{"key":"e_1_2_1_10_1","volume-title":"Proceedings of the 18th International Workshop on Randomization and Computation (RANDOM\u201914)","author":"Chattopadhyay Arkadev","year":"2014","unstructured":"Arkadev Chattopadhyay and Michael E. Saks . 2014. The power of super-logarithmic number of players . In Proceedings of the 18th International Workshop on Randomization and Computation (RANDOM\u201914) . 596--603. DOI:https:\/\/doi.org\/10.4230\/LIPIcs.APPROX-RANDOM. 2014 .596 10.4230\/LIPIcs.APPROX-RANDOM.2014.596 Arkadev Chattopadhyay and Michael E. Saks. 2014. The power of super-logarithmic number of players. In Proceedings of the 18th International Workshop on Randomization and Computation (RANDOM\u201914). 596--603. DOI:https:\/\/doi.org\/10.4230\/LIPIcs.APPROX-RANDOM.2014.596"},{"key":"e_1_2_1_11_1","doi-asserted-by":"publisher","DOI":"10.1137\/0217015"},{"key":"e_1_2_1_12_1","doi-asserted-by":"publisher","DOI":"10.1137\/0406009"},{"key":"e_1_2_1_14_1","first-page":"51","article-title":"The BNS lower bound for multi-party protocols in nearly optimal. Info","volume":"112","author":"Grolmusz Vince","year":"1994","unstructured":"Vince Grolmusz . 1994 . The BNS lower bound for multi-party protocols in nearly optimal. Info . Comput. 112 , 1 (1994), 51 -- 54 . DOI:https:\/\/doi.org\/10.1006\/inco.1994.1051 10.1006\/inco.1994.1051 Vince Grolmusz. 1994. The BNS lower bound for multi-party protocols in nearly optimal. Info. Comput. 112, 1 (1994), 51--54. DOI:https:\/\/doi.org\/10.1006\/inco.1994.1051","journal-title":"Comput."},{"key":"e_1_2_1_15_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF01272517"},{"volume-title":"Extremal Combinatorics with Applications in Computer Science","author":"Jukna Stasys","key":"e_1_2_1_16_1","unstructured":"Stasys Jukna . 2001. Extremal Combinatorics with Applications in Computer Science . Springer-Verlag , Berlin . DOI:https:\/\/doi.org\/10.1007\/978-3-662-04650-0 10.1007\/978-3-662-04650-0 Stasys Jukna. 2001. Extremal Combinatorics with Applications in Computer Science. Springer-Verlag, Berlin. DOI:https:\/\/doi.org\/10.1007\/978-3-662-04650-0"},{"key":"e_1_2_1_17_1","doi-asserted-by":"publisher","DOI":"10.1137\/0405044"},{"volume-title":"Communication Complexity","author":"Kushilevitz Eyal","key":"e_1_2_1_18_1","unstructured":"Eyal Kushilevitz and Noam Nisan . 1997. Communication Complexity . Cambridge University Press . Eyal Kushilevitz and Noam Nisan. 1997. Communication Complexity. 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DOI:https:\/\/doi.org\/10.1109\/FSCS.1990.89583"}],"container-title":["ACM Transactions on Computation Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3428671","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/3428671","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,17]],"date-time":"2025-06-17T22:01:59Z","timestamp":1750197719000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3428671"}},"subtitle":["Beyond Logarithmically Many Parties"],"short-title":[],"issued":{"date-parts":[[2020,11,25]]},"references-count":25,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2020,12,31]]}},"alternative-id":["10.1145\/3428671"],"URL":"https:\/\/doi.org\/10.1145\/3428671","relation":{},"ISSN":["1942-3454","1942-3462"],"issn-type":[{"type":"print","value":"1942-3454"},{"type":"electronic","value":"1942-3462"}],"subject":[],"published":{"date-parts":[[2020,11,25]]},"assertion":[{"value":"2018-01-01","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2020-08-01","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2020-11-25","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}