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In this work, we extend an existing tractability result to the three generalisations of CSPs combined: We give a sufficient condition for the combined basic linear programming and affine integer programming relaxation for exact solvability of promise valued CSPs over infinite-domains. This extends a result of Brakensiek and Guruswami\u00a0(SODA\u201920) for promise (non-valued) CSPs (on finite domains).<\/jats:p>","DOI":"10.1145\/3458041","type":"journal-article","created":{"date-parts":[[2021,7,16]],"date-time":"2021-07-16T05:26:33Z","timestamp":1626413193000},"page":"1-23","update-policy":"http:\/\/dx.doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":4,"title":["The Combined Basic LP and Affine IP Relaxation for Promise VCSPs on Infinite Domains"],"prefix":"10.1145","volume":"17","author":[{"given":"Caterina","family":"Viola","sequence":"first","affiliation":[{"name":"University of Oxford, United Kingdom"}]},{"given":"Stanislav","family":"\u017divn\u00fd","sequence":"additional","affiliation":[{"name":"University of Oxford, United Kingdom"}]}],"member":"320","published-online":{"date-parts":[[2021,7,15]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2007.02.016"},{"key":"e_1_2_1_2_1","first-page":"405","article-title":"Konvexe Funktionen und Induktion bei Ungleichungen zwischen Mittelverten. 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