{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,18]],"date-time":"2026-03-18T02:53:27Z","timestamp":1773802407074,"version":"3.50.1"},"reference-count":0,"publisher":"Association for the Advancement of Artificial Intelligence (AAAI)","issue":"17","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["AAAI"],"abstract":"<jats:p>The Aperiodic Tiling Complements Problem (ATCP) involves finding the full set of (normalized) aperiodic complements of a given pattern.\nThis has become a classic problem in music theory, with some recent attempts to model it using Integer Linear Programming (ILP) and Boolean Satisfiability (SAT) frameworks.\nIn this paper, we develop and compare different models of ATCP encoded with Constraint Programming (CP).\nThe most effective approach admits two phases: a first one that allows us to merge (join) several subsets of linear constraints under the form of tables with large arity, and a second one that advantageously exploits the generated tables to discard periodic tiling complements.\nOur experimental results show that our approach significantly outperforms the state-of-the-art, solving every instance of a classical benchmark (standard Vuza rhythms for canons with periods set up to 900) in a time between 5 seconds and 2 minutes (except the largest instance being solved in 18 minutes).<\/jats:p>","DOI":"10.1609\/aaai.v40i17.38434","type":"journal-article","created":{"date-parts":[[2026,3,18]],"date-time":"2026-03-18T00:33:00Z","timestamp":1773793980000},"page":"14209-14216","source":"Crossref","is-referenced-by-count":0,"title":["Aperiodic Tiling and Rhythmic Canons: A CP Journey"],"prefix":"10.1609","volume":"40","author":[{"given":"Guillaume","family":"Derval","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Christophe","family":"Lecoutre","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"9382","published-online":{"date-parts":[[2026,3,14]]},"container-title":["Proceedings of the AAAI Conference on Artificial Intelligence"],"original-title":[],"link":[{"URL":"https:\/\/ojs.aaai.org\/index.php\/AAAI\/article\/download\/38434\/42396","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/ojs.aaai.org\/index.php\/AAAI\/article\/download\/38434\/42396","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,3,18]],"date-time":"2026-03-18T00:33:00Z","timestamp":1773793980000},"score":1,"resource":{"primary":{"URL":"https:\/\/ojs.aaai.org\/index.php\/AAAI\/article\/view\/38434"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,3,14]]},"references-count":0,"journal-issue":{"issue":"17","published-online":{"date-parts":[[2026,3,17]]}},"URL":"https:\/\/doi.org\/10.1609\/aaai.v40i17.38434","relation":{},"ISSN":["2374-3468","2159-5399"],"issn-type":[{"value":"2374-3468","type":"electronic"},{"value":"2159-5399","type":"print"}],"subject":[],"published":{"date-parts":[[2026,3,14]]}}}