{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,1]],"date-time":"2026-03-01T11:53:45Z","timestamp":1772366025963,"version":"3.50.1"},"reference-count":19,"publisher":"Cambridge University Press (CUP)","issue":"2","license":[{"start":{"date-parts":[[2012,7,17]],"date-time":"2012-07-17T00:00:00Z","timestamp":1342483200000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Theory and Practice of Logic Programming"],"published-print":{"date-parts":[[2014,3]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Cardinality constraints or, more generally, weight constraints are well recognized as an important extension of answer-set programming. Clearly, all common algorithmic tasks related to programs with cardinality or weight constraints \u2013 like checking the consistency of a program \u2013 are intractable. Many intractable problems in the area of knowledge representation and reasoning have been shown to become linear time tractable if the treewidth of the programs or formulas under consideration is bounded by some constant. The goal of this paper is to apply the notion of treewidth to programs with cardinality or weight constraints and to identify tractable fragments. It will turn out that the straightforward application of treewidth to such class of programs does not suffice to obtain tractability. However, by imposing further restrictions, tractability can be achieved.<\/jats:p>","DOI":"10.1017\/s1471068412000099","type":"journal-article","created":{"date-parts":[[2012,7,17]],"date-time":"2012-07-17T15:53:17Z","timestamp":1342540397000},"page":"141-164","source":"Crossref","is-referenced-by-count":4,"title":["Tractable answer-set programming with weight constraints: bounded treewidth is not enough"],"prefix":"10.1017","volume":"14","author":[{"given":"REINHARD","family":"PICHLER","sequence":"first","affiliation":[]},{"given":"STEFAN","family":"R\u00dcMMELE","sequence":"additional","affiliation":[]},{"given":"STEFAN","family":"SZEIDER","sequence":"additional","affiliation":[]},{"given":"STEFAN","family":"WOLTRAN","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2012,7,17]]},"reference":[{"key":"S1471068412000099_ref19","doi-asserted-by":"publisher","DOI":"10.1007\/s00453-006-1226-x"},{"key":"S1471068412000099_ref11","volume-title":"Treewidth, Computations and Approximations","author":"Kloks","year":"1994"},{"key":"S1471068412000099_ref3","doi-asserted-by":"publisher","DOI":"10.1093\/comjnl\/bxm037"},{"key":"S1471068412000099_ref9","first-page":"816","volume-title":"Proceedings of the IJCAI '09","author":"Jakl","year":"2009"},{"key":"S1471068412000099_ref6","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-0515-9"},{"key":"S1471068412000099_ref18","doi-asserted-by":"publisher","DOI":"10.1145\/1877714.1877718"},{"key":"S1471068412000099_ref10","first-page":"54","volume-title":"Proceedings of the AAAI '11","author":"Kask","year":"2011"},{"key":"S1471068412000099_ref7","volume-title":"Parameterized Complexity Theory","author":"Flum","year":"2006"},{"key":"S1471068412000099_ref5","first-page":"1","volume-title":"Proceedings of the MICAI","author":"Dermaku","year":"2008"},{"key":"S1471068412000099_ref17","first-page":"179","volume-title":"Advances in Discrete Mathematics and Applications: Mysore, 2008","author":"Szeider","year":"2010"},{"key":"S1471068412000099_ref15","doi-asserted-by":"publisher","DOI":"10.1093\/acprof:oso\/9780198566076.001.0001"},{"key":"S1471068412000099_ref14","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-60085-2_17"},{"key":"S1471068412000099_ref8","doi-asserted-by":"publisher","DOI":"10.1016\/j.artint.2009.10.003"},{"key":"S1471068412000099_ref12","doi-asserted-by":"publisher","DOI":"10.1016\/S1571-0653(05)80078-2"},{"key":"S1471068412000099_ref4","volume-title":"Recognizability and Second-Order Definability for Sets of Finite Graphs","author":"Courcelle","year":"1987"},{"key":"S1471068412000099_ref2","doi-asserted-by":"publisher","DOI":"10.1016\/j.disc.2005.12.017"},{"key":"S1471068412000099_ref16","first-page":"317","volume-title":"Proceedings of the LPNMR'99","author":"Niemel\u00e4","year":"1999"},{"key":"S1471068412000099_ref1","doi-asserted-by":"publisher","DOI":"10.1137\/S0097539793251219"},{"key":"S1471068412000099_ref13","first-page":"444","volume-title":"Proceedings of the LPNMR '09","author":"Liu","year":"2009"}],"container-title":["Theory and Practice of Logic Programming"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S1471068412000099","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,4,22]],"date-time":"2019-04-22T22:53:32Z","timestamp":1555973612000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S1471068412000099\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,7,17]]},"references-count":19,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2014,3]]}},"alternative-id":["S1471068412000099"],"URL":"https:\/\/doi.org\/10.1017\/s1471068412000099","relation":{},"ISSN":["1471-0684","1475-3081"],"issn-type":[{"value":"1471-0684","type":"print"},{"value":"1475-3081","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,7,17]]}}}