{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T04:25:08Z","timestamp":1750220708691,"version":"3.41.0"},"reference-count":25,"publisher":"Association for Computing Machinery (ACM)","issue":"2","license":[{"start":{"date-parts":[[2020,3,9]],"date-time":"2020-03-09T00:00:00Z","timestamp":1583712000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"funder":[{"DOI":"10.13039\/501100003977","name":"Israel Science Foundation","doi-asserted-by":"crossref","award":["794\/13 and 592\/17"],"award-info":[{"award-number":["794\/13 and 592\/17"]}],"id":[{"id":"10.13039\/501100003977","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":[[2020,4,30]]},"abstract":"<jats:p>\n            We present an optimal data structure for submatrix maximum queries in\n            <jats:italic>n<\/jats:italic>\n            \u00d7\n            <jats:italic>n<\/jats:italic>\n            Monge matrices. Our result is a two-way reduction showing that the problem is equivalent to the classical predecessor problem in a universe of polynomial size. This gives a data structure of\n            <jats:italic>O<\/jats:italic>\n            (\n            <jats:italic>n<\/jats:italic>\n            ) space that answers submatrix maximum queries in\n            <jats:italic>O<\/jats:italic>\n            (log log\n            <jats:italic>n<\/jats:italic>\n            ) time, as well as a matching lower bound, showing that\n            <jats:italic>O<\/jats:italic>\n            (log log\n            <jats:italic>n<\/jats:italic>\n            ) query-time is optimal for any data structure of size\n            <jats:italic>O<\/jats:italic>\n            (\n            <jats:italic>n<\/jats:italic>\n            polylog(\n            <jats:italic>n<\/jats:italic>\n            )). Our result settles the problem, improving on the\n            <jats:italic>O<\/jats:italic>\n            (log\n            <jats:sup>2<\/jats:sup>\n            <jats:italic>n<\/jats:italic>\n            ) query time in SODA\u201912, and on the\n            <jats:italic>O<\/jats:italic>\n            (log\n            <jats:italic>n<\/jats:italic>\n            ) query-time in ICALP\u201914.\n          <\/jats:p>\n          <jats:p>In addition, we show that partial Monge matrices can be handled in the same bounds as full Monge matrices. In both previous results, partial Monge matrices incurred additional inverse-Ackermann factors.<\/jats:p>","DOI":"10.1145\/3381416","type":"journal-article","created":{"date-parts":[[2020,3,9]],"date-time":"2020-03-09T21:33:40Z","timestamp":1583789620000},"page":"1-24","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":1,"title":["Submatrix Maximum Queries in Monge and Partial Monge Matrices Are Equivalent to Predecessor Search"],"prefix":"10.1145","volume":"16","author":[{"given":"Pawe\u0142","family":"Gawrychowski","sequence":"first","affiliation":[{"name":"University of Wroc\u0142aw, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9262-1821","authenticated-orcid":false,"given":"Shay","family":"Mozes","sequence":"additional","affiliation":[{"name":"Interdisciplinary Center Herzliya, Israel"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Oren","family":"Weimann","sequence":"additional","affiliation":[{"name":"University of Haifa, Israel"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2020,3,9]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"publisher","DOI":"10.1016\/0166-218X(90)90124-U"},{"key":"e_1_2_1_2_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF01840359"},{"volume-title":"Proceedings of the 41st FOCS Symposium. 198--207","author":"Alstrup S.","key":"e_1_2_1_3_1"},{"volume-title":"Proceedings of the 18th CPM Symposium. 286--294","author":"Amir A.","key":"e_1_2_1_4_1"},{"volume-title":"Proceedings of the 20th ESA. 217--228","author":"Brodal G. 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