{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,28]],"date-time":"2025-11-28T17:20:40Z","timestamp":1764350440312,"version":"3.41.0"},"reference-count":28,"publisher":"Association for Computing Machinery (ACM)","issue":"1","license":[{"start":{"date-parts":[[2018,3,31]],"date-time":"2018-03-31T00:00:00Z","timestamp":1522454400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61722207&61672275"],"award-info":[{"award-number":["61722207&61672275"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Parallel Comput."],"published-print":{"date-parts":[[2018,3,31]]},"abstract":"<jats:p>\n            We study the complexity of parallel data structures for approximate nearest neighbor search in\n            <jats:italic>d<\/jats:italic>\n            -dimensional Hamming space {0,1}\n            <jats:sup>\n              <jats:italic>d<\/jats:italic>\n            <\/jats:sup>\n            . A classic model for static data structures is the cell-probe model\u00a0[27]. We consider a cell-probe model with limited\n            <jats:italic>adaptivity<\/jats:italic>\n            , where given a\n            <jats:italic>k<\/jats:italic>\n            \u22651, a query is resolved by making at most\n            <jats:italic>k<\/jats:italic>\n            rounds of parallel memory accesses to the data structure. We give two randomized algorithms that solve the approximate nearest neighbor search using\n            <jats:italic>k<\/jats:italic>\n            rounds of parallel memory accesses:\n          <\/jats:p>\n          <jats:p>\n            \u2014a simple algorithm with\n            <jats:italic>O<\/jats:italic>\n            (\n            <jats:italic>k<\/jats:italic>\n            (log\n            <jats:italic>d<\/jats:italic>\n            )\n            <jats:sup>\n              1\/\n              <jats:italic>k<\/jats:italic>\n            <\/jats:sup>\n            ) total number of memory accesses for all\n            <jats:italic>k<\/jats:italic>\n            \u22651;\n          <\/jats:p>\n          <jats:p>\n            \u2014an algorithm with\n            <jats:italic>O<\/jats:italic>\n            (\n            <jats:italic>k<\/jats:italic>\n            +(1\/\n            <jats:italic>k<\/jats:italic>\n            log\n            <jats:italic>d<\/jats:italic>\n            )\n            <jats:sup>\n              <jats:italic>O<\/jats:italic>\n              (1\/\n              <jats:italic>k<\/jats:italic>\n              )\n            <\/jats:sup>\n            ) total number of memory accesses for all sufficiently large\n            <jats:italic>k<\/jats:italic>\n            .\n          <\/jats:p>\n          <jats:p>Both algorithms use data structures of polynomial size.<\/jats:p>\n          <jats:p>\n            We prove an \u03a9(1\/\n            <jats:italic>k<\/jats:italic>\n            (log\n            <jats:italic>d<\/jats:italic>\n            )\n            <jats:sup>\n              1\/\n              <jats:italic>k<\/jats:italic>\n            <\/jats:sup>\n            ) lower bound for the total number of memory accesses for any randomized algorithm solving the approximate nearest neighbor search within\n            <jats:italic>k<\/jats:italic>\n            \u2264log log\n            <jats:italic>d<\/jats:italic>\n            \/2log log log\n            <jats:italic>d<\/jats:italic>\n            rounds of parallel memory accesses on any data structures of polynomial size. This lower bound shows that our first algorithm is asymptotically optimal when\n            <jats:italic>k<\/jats:italic>\n            =\n            <jats:italic>O<\/jats:italic>\n            (1). And our second algorithm achieves the asymptotically optimal tradeoff between number of rounds and total number of memory accesses. In the extremal case, when\n            <jats:italic>k<\/jats:italic>\n            =\n            <jats:italic>O<\/jats:italic>\n            (log log\n            <jats:italic>d<\/jats:italic>\n            \/log log log\n            <jats:italic>d<\/jats:italic>\n            ) is big enough, our second algorithm matches the \u0398(log log\n            <jats:italic>d<\/jats:italic>\n            \/log log log\n            <jats:italic>d<\/jats:italic>\n            ) tight bound for fully adaptive algorithms for approximate nearest neighbor search in\u00a0[11].\n          <\/jats:p>","DOI":"10.1145\/3209884","type":"journal-article","created":{"date-parts":[[2018,6,15]],"date-time":"2018-06-15T14:14:38Z","timestamp":1529072078000},"page":"1-26","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":2,"title":["Randomized Approximate Nearest Neighbor Search with Limited Adaptivity"],"prefix":"10.1145","volume":"5","author":[{"given":"Mingmou","family":"Liu","sequence":"first","affiliation":[{"name":"Nanjing University, China, Xianlin Ave., Nanjing, Jiangsu, China"}]},{"given":"Xiaoyin","family":"Pan","sequence":"additional","affiliation":[{"name":"Nanjing University, China, Xianlin Ave., Nanjing, Jiangsu, China"}]},{"given":"Yitong","family":"Yin","sequence":"additional","affiliation":[{"name":"Nanjing University, China, Xianlin Ave., Nanjing, Jiangsu, China"}]}],"member":"320","published-online":{"date-parts":[[2018,6,13]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF02126797"},{"key":"e_1_2_1_2_1","doi-asserted-by":"publisher","DOI":"10.1109\/FOCS.2006.49"},{"edition":"3","volume-title":"Handbook of Discrete and Computational Geometry","author":"Andoni Alexandr","key":"e_1_2_1_3_1"},{"key":"e_1_2_1_4_1","doi-asserted-by":"publisher","DOI":"10.5555\/2634074.2634150"},{"key":"e_1_2_1_5_1","doi-asserted-by":"publisher","DOI":"10.1145\/2746539.2746553"},{"key":"e_1_2_1_6_1","doi-asserted-by":"publisher","DOI":"10.1145\/1810479.1810539"},{"key":"e_1_2_1_7_1","doi-asserted-by":"publisher","DOI":"10.1145\/335305.335350"},{"key":"e_1_2_1_8_1","doi-asserted-by":"publisher","DOI":"10.1145\/301250.301330"},{"key":"e_1_2_1_9_1","doi-asserted-by":"publisher","DOI":"10.4086\/toc.2015.v011a019"},{"volume-title":"Discrete and Computational Geometry","author":"Chakrabarti Amit","key":"e_1_2_1_10_1"},{"key":"e_1_2_1_11_1","doi-asserted-by":"publisher","DOI":"10.5555\/1958016.1958025"},{"key":"e_1_2_1_12_1","doi-asserted-by":"crossref","unstructured":"Piotr Indyk. 2004. 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