{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,5]],"date-time":"2025-10-05T04:35:25Z","timestamp":1759638925127,"version":"3.41.0"},"reference-count":24,"publisher":"Association for Computing Machinery (ACM)","issue":"3","license":[{"start":{"date-parts":[[2018,6,16]],"date-time":"2018-06-16T00:00:00Z","timestamp":1529107200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"funder":[{"name":"Australian Research Council\u2019s Discovery Projects funding scheme","award":["DP150101134"],"award-info":[{"award-number":["DP150101134"]}]},{"DOI":"10.13039\/501100003246","name":"Netherlands\u2019 Organisation for Scientific Research","doi-asserted-by":"crossref","award":["024.002.003 and 022.005.025"],"award-info":[{"award-number":["024.002.003 and 022.005.025"]}],"id":[{"id":"10.13039\/501100003246","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Algorithms"],"published-print":{"date-parts":[[2018,7,31]]},"abstract":"<jats:p>\n            Let\n            <jats:italic>V<\/jats:italic>\n            be a set of\n            <jats:italic>n<\/jats:italic>\n            points in R\n            <jats:sup>\n              <jats:italic>d<\/jats:italic>\n            <\/jats:sup>\n            , which we call voters. A point\n            <jats:italic>p<\/jats:italic>\n            \u2208 R\n            <jats:sup>\n              <jats:italic>d<\/jats:italic>\n            <\/jats:sup>\n            is preferred over another point\n            <jats:italic>p<\/jats:italic>\n            \u2032 \u2208 R\n            <jats:sup>\n              <jats:italic>d<\/jats:italic>\n            <\/jats:sup>\n            by a voter \u03c5 \u2208\n            <jats:italic>V<\/jats:italic>\n            if dist(\u03c5,\n            <jats:italic>p<\/jats:italic>\n            ) &lt; dist(\u03c5,\n            <jats:italic>p<\/jats:italic>\n            \u2032). A point\n            <jats:italic>p<\/jats:italic>\n            is called a plurality point if it is preferred by at least as many voters as any other point\u00a0\n            <jats:italic>p<\/jats:italic>\n            \u2032.\n          <\/jats:p>\n          <jats:p>\n            We present an algorithm that decides in\n            <jats:italic>O<\/jats:italic>\n            (\n            <jats:italic>n<\/jats:italic>\n            log\n            <jats:italic>n<\/jats:italic>\n            ) time whether\n            <jats:italic>V<\/jats:italic>\n            admits a plurality point in the\n            <jats:italic>L<\/jats:italic>\n            <jats:sub>2<\/jats:sub>\n            norm and, if so, finds the (unique) plurality point. We also give efficient algorithms to compute a minimum-cost subset\n            <jats:italic>W<\/jats:italic>\n            \u2282\n            <jats:italic>V<\/jats:italic>\n            such that\n            <jats:italic>V<\/jats:italic>\n            \\\n            <jats:italic>W<\/jats:italic>\n            admits a plurality point, and to compute a so-called minimum-radius plurality ball.\n          <\/jats:p>\n          <jats:p>\n            Finally, we consider the problem in the personalized\n            <jats:italic>L<\/jats:italic>\n            <jats:sub>1<\/jats:sub>\n            norm, where each point \u03c5 \u2208\n            <jats:italic>V<\/jats:italic>\n            has a preference vector \u2329\n            <jats:italic>w<\/jats:italic>\n            <jats:sub>1<\/jats:sub>\n            (\u03c5),\u2026,\n            <jats:italic>w<\/jats:italic>\n            <jats:sub>\n              <jats:italic>d<\/jats:italic>\n            <\/jats:sub>\n            (\u03c5)\u232a and the distance from \u03c5 to any point\n            <jats:italic>p<\/jats:italic>\n            \u2208 R\n            <jats:sup>\n              <jats:italic>d<\/jats:italic>\n            <\/jats:sup>\n            is given by \u2211\n            <jats:sub>\n              <jats:italic>i<\/jats:italic>\n              =1\n            <\/jats:sub>\n            <jats:sup>\n              <jats:italic>d<\/jats:italic>\n            <\/jats:sup>\n            <jats:italic>w<\/jats:italic>\n            <jats:sub>\n              <jats:italic>i<\/jats:italic>\n            <\/jats:sub>\n            (\u03c5)\u00b7 |\n            <jats:italic>x<\/jats:italic>\n            <jats:sub>\n              <jats:italic>i<\/jats:italic>\n            <\/jats:sub>\n            (\u03c5)\u2212\n            <jats:italic>x<\/jats:italic>\n            <jats:sub>\n              <jats:italic>i<\/jats:italic>\n            <\/jats:sub>\n            (\n            <jats:italic>p<\/jats:italic>\n            )|. For this case we can compute in\n            <jats:italic>O<\/jats:italic>\n            (\n            <jats:italic>n<\/jats:italic>\n            <jats:sup>\n              <jats:italic>d<\/jats:italic>\n              \u22121\n            <\/jats:sup>\n            ) time the set of all plurality points of\u00a0\n            <jats:italic>V<\/jats:italic>\n            . When all preference vectors are equal, the running time improves to\n            <jats:italic>O<\/jats:italic>\n            (\n            <jats:italic>n<\/jats:italic>\n            ).\n          <\/jats:p>","DOI":"10.1145\/3186990","type":"journal-article","created":{"date-parts":[[2018,6,18]],"date-time":"2018-06-18T12:28:11Z","timestamp":1529324891000},"page":"1-23","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":3,"title":["Faster Algorithms for Computing Plurality Points"],"prefix":"10.1145","volume":"14","author":[{"given":"Mark De","family":"Berg","sequence":"first","affiliation":[{"name":"TU Eindhoven, The Netherlands"}]},{"given":"Joachim","family":"Gudmundsson","sequence":"additional","affiliation":[{"name":"University of Sydney, Australia"}]},{"given":"Mehran","family":"Mehr","sequence":"additional","affiliation":[{"name":"TU Eindhoven, The Netherlands"}]}],"member":"320","published-online":{"date-parts":[[2018,6,16]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.tcs.2003.09.004"},{"key":"e_1_2_1_2_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF02574379"},{"key":"e_1_2_1_3_1","doi-asserted-by":"publisher","DOI":"10.1145\/800061.808735"},{"key":"e_1_2_1_4_1","volume-title":"Proc. 15th ACM-SIAM Symp. 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