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We propose a novel and computationally efficient solution, called ONe Index for All Kernels (ONIAK), to ANNS-ALT and all its baby problems when the data dimension\n            <jats:italic>d<\/jats:italic>\n            is not too large (say\n            <jats:italic>d<\/jats:italic>\n            \u2264 200). In ONIAK, a universal index is built, once and for all, for answering all future ANNS-ALT queries that can have\n            <jats:italic>distinct<\/jats:italic>\n            query matrices. We show by experiments that, when\n            <jats:italic>d<\/jats:italic>\n            is not too large, ONIAK has better query performance than linear scan on the mother problem (of ANNS-ALT), and has query performances comparable to those of the state-of-the-art solutions on the baby problems. However, the algorithmic technique behind this universal index approach suffers from a so-called dimension blowup problem that can make the indexing time prohibitively long for a large dataset. We propose a novel algorithmic technique, called fast GOE quadratic form (FGoeQF), that completely solves the (prohibitively long indexing time) fallout of the dimension blowup problem. We also propose a Johnson-Lindenstrauss transform (JLT) based ANNS-ALT (and ANNS-ALTD) solution that significantly outperforms any competitor when\n            <jats:italic>d<\/jats:italic>\n            is large.\n          <\/jats:p>","DOI":"10.14778\/3565838.3565847","type":"journal-article","created":{"date-parts":[[2023,1,20]],"date-time":"2023-01-20T23:09:56Z","timestamp":1674256196000},"page":"3937-3949","update-policy":"http:\/\/dx.doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":3,"title":["ONe Index for All Kernels (ONIAK)"],"prefix":"10.14778","volume":"15","author":[{"given":"Jingfan","family":"Meng","sequence":"first","affiliation":[{"name":"Georgia Institute of Technology"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Huayi","family":"Wang","sequence":"additional","affiliation":[{"name":"Georgia Institute of Technology"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jun","family":"Xu","sequence":"additional","affiliation":[{"name":"Georgia Institute of Technology"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mitsunori","family":"Ogihara","sequence":"additional","affiliation":[{"name":"University of Miami"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2023,1,20]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-45450-9_6"},{"key":"e_1_2_1_2_1","doi-asserted-by":"publisher","DOI":"10.1137\/060673096"},{"key":"e_1_2_1_3_1","unstructured":"Bruce Alberts Alexander Johnson Julian Lewis Martin Raff Keith Roberts and Peter. 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