{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T07:44:48Z","timestamp":1740123888286,"version":"3.37.3"},"reference-count":24,"publisher":"Springer Science and Business Media LLC","issue":"10","license":[{"start":{"date-parts":[[2020,9,15]],"date-time":"2020-09-15T00:00:00Z","timestamp":1600128000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2020,9,15]],"date-time":"2020-09-15T00:00:00Z","timestamp":1600128000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Ann Math Artif Intell"],"published-print":{"date-parts":[[2020,10]]},"DOI":"10.1007\/s10472-020-09703-5","type":"journal-article","created":{"date-parts":[[2020,9,15]],"date-time":"2020-09-15T10:03:01Z","timestamp":1600164181000},"page":"1101-1118","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["On integer closure in a system of unit two variable per inequality constraints"],"prefix":"10.1007","volume":"88","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5821-5117","authenticated-orcid":false,"given":"K.","family":"Subramani","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"P.","family":"Wojciechowski","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2020,9,15]]},"reference":[{"issue":"3","key":"9703_CR1","doi-asserted-by":"publisher","first-page":"279","DOI":"10.1007\/s10703-009-0073-1","volume":"35","author":"R Bagnara","year":"2009","unstructured":"Bagnara, R., Hill, P.M., Zaffanella, E.: Weakly-relational shapes for numeric abstractions: Improved algorithms and proofs of correctness. Formal Methods in System Design (FMSD) 35(3), 279\u2013323 (2009)","journal-title":"Formal Methods in System Design (FMSD)"},{"key":"9703_CR2","volume-title":"Introduction to Algorithms","author":"TH Cormen","year":"2009","unstructured":"Cormen, T.H., Leiserson, C.E., Rivest, R.L., Stein, C.: Introduction to Algorithms, 3rd edn. The MIT Press, Cambridge (2009)","edition":"3rd edn"},{"doi-asserted-by":"crossref","unstructured":"Cousot, P., Cousot, R.: Abstract interpretation: a unified lattice model for static analysis of programs by construction or approximation of fixpoints. In: Proceedings of the Symposium on Principles of Programming Languages (POPL), pp. 238\u2013252 (1977)","key":"9703_CR3","DOI":"10.1145\/512950.512973"},{"key":"9703_CR4","doi-asserted-by":"publisher","first-page":"288","DOI":"10.1016\/0097-3165(73)90004-6","volume":"14","author":"GB Dantzig","year":"1973","unstructured":"Dantzig, G.B., Eaves, B.C.: Fourier-motzkin Elimination and its Dual. Journal of Combinatorial Theory (A) 14, 288\u2013297 (1973)","journal-title":"Journal of Combinatorial Theory (A)"},{"key":"9703_CR5","volume-title":"Constraint Processing","author":"R Dechter","year":"2003","unstructured":"Dechter, R.: Constraint Processing. Morgan Kaufmann Publishers Inc., San Francisco (2003)"},{"issue":"3","key":"9703_CR6","doi-asserted-by":"publisher","first-page":"471","DOI":"10.1109\/12.372041","volume":"44","author":"R Gerber","year":"1995","unstructured":"Gerber, R., Pugh, W., Saksena, M.: Parametric dispatching of hard real-time tasks. IEEE Trans. Comput. 44(3), 471\u2013479 (1995)","journal-title":"IEEE Trans. Comput."},{"unstructured":"Harvey, W., Stuckey, P. J.: A unit two variable per inequality integer constraint solver for constraint logic programming. In: Proceedings of the 20th Australasian Computer Science Conference (ACSC), pp. 102\u2013111 (1997)","key":"9703_CR7"},{"issue":"6","key":"9703_CR8","doi-asserted-by":"publisher","first-page":"1179","DOI":"10.1137\/S0097539793251876","volume":"23","author":"DS Hochbaum","year":"1994","unstructured":"Hochbaum, DS, Naor, JS: Simple and fast algorithms for linear and integer programs with two variables per inequality. SIAM J. Comput. 23(6), 1179\u20131192 (1994)","journal-title":"SIAM J. Comput."},{"doi-asserted-by":"crossref","unstructured":"Jaffar, J., Maher, M.J., Stuckey, P.J., Yap, H.C.: Beyond finite domains. In: Proceedings of the Second International Workshop on Principles and Practice of Constraint Programming (PPCP) (1994)","key":"9703_CR9","DOI":"10.1007\/3-540-58601-6_92"},{"doi-asserted-by":"crossref","unstructured":"Lahiri, S.K., Musuvathi, M.: An efficient decision procedure for UTVPI constraints. In: Proceedings of the 5th International Workshop on the Frontiers of Combining Systems (FroCos) (2005)","key":"9703_CR10","DOI":"10.1007\/11559306_9"},{"issue":"1","key":"9703_CR11","doi-asserted-by":"publisher","first-page":"31","DOI":"10.1007\/s10990-006-8609-1","volume":"19","author":"A Min\u00e9","year":"2006","unstructured":"Min\u00e9, A.: The octagon abstract domain. Higher-Order and Symbolic Computation 19(1), 31\u2013100 (2006)","journal-title":"Higher-Order and Symbolic Computation"},{"doi-asserted-by":"crossref","unstructured":"Nieuwenhuis, R., Oliveras, A., Tinelli, C.: Abstract DPLL and abstract DPLL modulo theories. In: Proceedings of the 11th International Conference on Logic for Programming (LPAR), pp. 36\u201350 (2004)","key":"9703_CR12","DOI":"10.1007\/978-3-540-32275-7_3"},{"key":"9703_CR13","volume-title":"Theory of Linear and Integer Programming","author":"A Schrijver","year":"1987","unstructured":"Schrijver, A.: Theory of Linear and Integer Programming. Wiley, New York (1987)"},{"issue":"4","key":"9703_CR14","doi-asserted-by":"publisher","first-page":"514","DOI":"10.1287\/ijoc.1090.0369","volume":"22","author":"A Schutt","year":"2010","unstructured":"Schutt, A., Stuckey, PJ.: Incremental satisfiability and implication for utvpi constraints. Informs J. Comput. 22(4), 514\u2013527 (2010)","journal-title":"Informs J. Comput."},{"doi-asserted-by":"crossref","unstructured":"Simon, A., King, A., Howe, J.M.: Two variables per linear inequality as an abstract domain. In: Proceedings of the 12th International Workshop on Logic Based Program Synthesis and Tranformation (LOPSTR), pp. 71\u201389 (2002)","key":"9703_CR15","DOI":"10.1007\/3-540-45013-0_7"},{"unstructured":"Sitzmann, I., Stuckey, P.J.: O-trees: a constraint-based index structure. In: Proceedings of the 11th Australasian Database Conference (ADC), pp. 127\u2013134 (2000)","key":"9703_CR16"},{"issue":"3","key":"9703_CR17","doi-asserted-by":"publisher","first-page":"281","DOI":"10.1002\/malq.200310099","volume":"50","author":"K Subramani","year":"2004","unstructured":"Subramani, K.: On deciding the non-emptiness of 2SAT polytopes with respect to first order queries. Math. Log. Q. 50(3), 281\u2013292 (2004)","journal-title":"Math. Log. Q."},{"doi-asserted-by":"crossref","unstructured":"Subramani, K., Wojciechowski, P.J.: A bit-scaling algorithm for integer feasibility in UTVPI constraints. In: Proceedings of the 27th International Workshop on Combinatorial Algorithms (IWOCA), vol. 9843, pp. 321\u2013333 (2016)","key":"9703_CR18","DOI":"10.1007\/978-3-319-44543-4_25"},{"doi-asserted-by":"crossref","unstructured":"Subramani, K., Wojciechowski, P.J.: An optimal algorithm for computing the integer closure of UTVPI constraints. In: Proceedings of the 10th International Workshop on Algorithms and Computation (WALCOM), vol. 9627 of Lecture Notes in Computer Science, pp 154\u2013165. Springer, berlin (2016)","key":"9703_CR19","DOI":"10.1007\/978-3-319-30139-6_13"},{"doi-asserted-by":"crossref","unstructured":"Subramani, K., Wojciechowski, P.J.: Analyzing lattice point feasibility in UTVPI constraints. In: Proceedings of the 23rd International Conference on Principles and Practice of Constraint Programming (CP), pp. 615\u2013629 (2017)","key":"9703_CR20","DOI":"10.1007\/978-3-319-66158-2_39"},{"issue":"1","key":"9703_CR21","doi-asserted-by":"publisher","first-page":"166","DOI":"10.1007\/s00453-016-0131-1","volume":"78","author":"K Subramani","year":"2017","unstructured":"Subramani, K., Wojciechowski, P.J.: A combinatorial certifying algorithm for linear feasibility in UTVPI constraints. Algorithmica 78(1), 166\u2013208 (2017)","journal-title":"Algorithmica"},{"issue":"2","key":"9703_CR22","doi-asserted-by":"publisher","first-page":"389","DOI":"10.1007\/s10878-017-0176-3","volume":"35","author":"K Subramani","year":"2018","unstructured":"Subramani, K., Wojciechowski, P.J.: A certifying algorithm for lattice point feasibility in a system of UTVPI constraints. J. Comb. Optim. 35(2), 389\u2013408 (2018)","journal-title":"J. Comb. Optim."},{"doi-asserted-by":"crossref","unstructured":"Wojciechowski, P.J., Subramani, K., Williamson, M.D.: Optimal length tree-like refutations of linear feasibility in UTVPI constraints. In: Proceedings of the 12th International Workshop on Frontiers in Algorithmics(FAW), vol. 10923, pp. 300\u2013314 (2018)","key":"9703_CR23","DOI":"10.1007\/978-3-319-78455-7_23"},{"issue":"7","key":"9703_CR24","doi-asserted-by":"publisher","first-page":"2765","DOI":"10.1007\/s00453-019-00554-z","volume":"81","author":"K Subramani","year":"2019","unstructured":"Subramani, K., Wojciechowki, P.: A polynomial time algorithm for read-once certification of linear infeasibility in UTVPI constraints. Algorithmica 81 (7), 2765\u20132794 (2019)","journal-title":"Algorithmica"}],"container-title":["Annals of Mathematics and Artificial Intelligence"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10472-020-09703-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10472-020-09703-5\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10472-020-09703-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,9,15]],"date-time":"2021-09-15T00:50:35Z","timestamp":1631667035000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10472-020-09703-5"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,9,15]]},"references-count":24,"journal-issue":{"issue":"10","published-print":{"date-parts":[[2020,10]]}},"alternative-id":["9703"],"URL":"https:\/\/doi.org\/10.1007\/s10472-020-09703-5","relation":{},"ISSN":["1012-2443","1573-7470"],"issn-type":[{"type":"print","value":"1012-2443"},{"type":"electronic","value":"1573-7470"}],"subject":[],"published":{"date-parts":[[2020,9,15]]},"assertion":[{"value":"15 September 2020","order":1,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}