{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,18]],"date-time":"2026-08-18T14:59:14Z","timestamp":1787065154280,"version":"build-2736575974"},"reference-count":24,"publisher":"Association for Computing Machinery (ACM)","issue":"3","license":[{"start":{"date-parts":[[2016,12,15]],"date-time":"2016-12-15T00:00:00Z","timestamp":1481760000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Inf. Syst."],"published-print":{"date-parts":[[2017,7,31]]},"abstract":"<jats:p>Most research into similarity search in metric spaces relies on the triangle inequality property. This property allows the space to be arranged according to relative distances to avoid searching some subspaces. We show that many common metric spaces, notably including those using Euclidean and Jensen-Shannon distances, also have a stronger property, sometimes called the four-point property: In essence, these spaces allow an isometric embedding of any four points in three-dimensional Euclidean space, as well as any three points in two-dimensional Euclidean space. In fact, we show that any space that is isometrically embeddable in Hilbert space has the stronger property. This property gives stronger geometric guarantees, and one in particular, which we name the Hilbert Exclusion property, allows any indexing mechanism which uses hyperplane partitioning to perform better. One outcome of this observation is that a number of state-of-the-art indexing mechanisms over high-dimensional spaces can be easily refined to give a significant increase in performance; furthermore, the improvement given is greater in higher dimensions. This therefore leads to a significant improvement in the cost of metric search in these spaces.<\/jats:p>","DOI":"10.1145\/3001583","type":"journal-article","created":{"date-parts":[[2016,12,15]],"date-time":"2016-12-15T12:50:23Z","timestamp":1481806223000},"page":"1-27","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":23,"title":["Hilbert Exclusion"],"prefix":"10.1145","volume":"35","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4734-8103","authenticated-orcid":false,"given":"Richard","family":"Connor","sequence":"first","affiliation":[{"name":"University of Strathclyde, Computer and Information Sciences, Glasgow, United Kingdom"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Franco Alberto","family":"Cardillo","sequence":"additional","affiliation":[{"name":"National Research Council of Italy (CNR), Institute for Computational Linguistics, Pisa, Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7182-7038","authenticated-orcid":false,"given":"Lucia","family":"Vadicamo","sequence":"additional","affiliation":[{"name":"National Research Council of Italy (CNR), Information Science and Technology Institute (ISTI), Pisa, Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Fausto","family":"Rabitti","sequence":"additional","affiliation":[{"name":"National Research Council of Italy (CNR), Information Science and Technology Institute (ISTI), Pisa, Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"320","published-online":{"date-parts":[[2016,12,15]]},"reference":[{"key":"e_1_2_1_1_1","volume-title":"Andre Nikolaevich Kolmogorov, and Mikhail Alekseevich Lavrent\u2019ev","author":"Aleksandrov Aleksandr Danilovich","year":"1999","unstructured":"Aleksandr Danilovich Aleksandrov , Andre Nikolaevich Kolmogorov, and Mikhail Alekseevich Lavrent\u2019ev . 1999 . Mathematics : Its Content, Methods and Meaning (Dover Books on Mathematics). Dover Publications . Aleksandr Danilovich Aleksandrov, Andre Nikolaevich Kolmogorov, and Mikhail Alekseevich Lavrent\u2019ev. 1999. Mathematics: Its Content, Methods and Meaning (Dover Books on Mathematics). Dover Publications."},{"key":"e_1_2_1_2_1","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9904-1933-05654-9"},{"key":"e_1_2_1_3_1","volume-title":"Theory and Applications of Distance Geometry","author":"Blumenthal Leonard M.","unstructured":"Leonard M. Blumenthal . 1953. Theory and Applications of Distance Geometry . Clarendon Press . Leonard M. Blumenthal. 1953. Theory and Applications of Distance Geometry. 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