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However, current solvers employing unsatisfiable core analysis either run to completion, or provide no suboptimal stable models but the one resulting from the preliminary disjoint cores analysis. This drawback is circumvented here by introducing a progression based shrinking of the analyzed unsatisfiable cores. In fact, suboptimal stable models are possibly found while shrinking unsatisfiable cores, hence resulting into an anytime algorithm. Moreover, as confirmed empirically, unsatisfiable core analysis also benefits from the shrinking process in terms of solved instances.<\/jats:p>","DOI":"10.1017\/s147106841600020x","type":"journal-article","created":{"date-parts":[[2016,10,15]],"date-time":"2016-10-15T21:28:20Z","timestamp":1476566900000},"page":"533-551","source":"Crossref","is-referenced-by-count":26,"title":["Anytime answer set optimization via unsatisfiable core shrinking"],"prefix":"10.1017","volume":"16","author":[{"given":"MARIO","family":"ALVIANO","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5617-5286","authenticated-orcid":false,"given":"CARMINE","family":"DODARO","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2016,10,14]]},"reference":[{"key":"S147106841600020X_ref34","doi-asserted-by":"publisher","DOI":"10.1016\/j.artint.2009.11.016"},{"key":"S147106841600020X_ref44","doi-asserted-by":"publisher","DOI":"10.1016\/S0004-3702(02)00187-X"},{"key":"S147106841600020X_ref29","doi-asserted-by":"publisher","DOI":"10.1017\/S1471068414000222"},{"key":"S147106841600020X_ref10","doi-asserted-by":"publisher","DOI":"10.1017\/S147106841500023X"},{"key":"S147106841600020X_ref31","first-page":"346","volume-title":"Logic Programming and Nonmonotonic Reasoning, 7th International Conference, LPNMR 2004, Fort Lauderdale, FL, USA, January 6-8, 2004, Proceedings","author":"Lierler","year":"2004"},{"key":"S147106841600020X_ref27","first-page":"531","volume-title":"Proceedings of Logic Programming and Nonmonotonic Reasoning - 13th International Conference, LPNMR 2015","author":"Gebser","year":"2015"},{"key":"S147106841600020X_ref5","first-page":"2677","volume-title":"Proceedings of the Twenty-Fourth International Joint Conference on Artificial Intelligence, IJCAI 2015","author":"Alviano","year":"2015"},{"key":"S147106841600020X_ref37","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-79719-7_21"},{"key":"S147106841600020X_ref33","volume-title":"Principles of Knowledge Representation and Reasoning: Proceedings of the Thirteenth International Conference, KR 2012","author":"Liu","year":"2012"},{"key":"S147106841600020X_ref32","first-page":"1594","volume-title":"Proceedings of the Twenty-Third AAAI Conference on Artificial Intelligence, AAAI 2008","author":"Lifschitz","year":"2008"},{"key":"S147106841600020X_ref15","volume-title":"Proceedings of the Twenty-Fifth International Joint Conference on Artificial Intelligence, IJCAI 2016","author":"Bliem","year":"2016"},{"key":"S147106841600020X_ref19","unstructured":"Dodaro C. , Alviano M. , Faber W. , Leone N. , Ricca F. and Sirianni M. 2011. 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