{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,31]],"date-time":"2025-10-31T07:13:46Z","timestamp":1761894826526},"reference-count":30,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2008,12,24]],"date-time":"2008-12-24T00:00:00Z","timestamp":1230076800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J Glob Optim"],"published-print":{"date-parts":[[2009,12]]},"DOI":"10.1007\/s10898-008-9386-7","type":"journal-article","created":{"date-parts":[[2008,12,23]],"date-time":"2008-12-23T06:10:50Z","timestamp":1230012650000},"page":"499-531","source":"Crossref","is-referenced-by-count":15,"title":["Interval propagation and search on directed acyclic graphs for numerical constraint solving"],"prefix":"10.1007","volume":"45","author":[{"given":"Xuan-Ha","family":"Vu","sequence":"first","affiliation":[],"role":[{"role":"author","vocab":"crossref"}]},{"given":"Hermann","family":"Schichl","sequence":"additional","affiliation":[],"role":[{"role":"author","vocab":"crossref"}]},{"given":"Djamila","family":"Sam-Haroud","sequence":"additional","affiliation":[],"role":[{"role":"author","vocab":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2008,12,24]]},"reference":[{"key":"9386_CR1","volume-title":"Introduction to Interval Computations","author":"G. Alefeld","year":"1983","unstructured":"Alefeld G., Herzberger J.: Introduction to Interval Computations. Academic Press, New York (1983)"},{"key":"9386_CR2","doi-asserted-by":"crossref","unstructured":"Benhamou, F., Older, W.J.: Applying interval arithmetic to real, integer and boolean constraints. J. Log. Programm, pp. 32\u201381, 1997. Extension of a Technical Report of Bell Northern Research, Canada (1992)","DOI":"10.1016\/S0743-1066(96)00142-2"},{"key":"9386_CR3","unstructured":"Benhamou, F., Older, W.J.: Applying interval arithmetic to real, integer and boolean constraints. Technical Report BNR, Technical Report, Bell Northern Research, ON, Canada (1992)"},{"key":"9386_CR4","unstructured":"Benhamou, F., McAllester, D., Van Hentenryck, P.: CLP(Intervals) revisited. In: Proceedings of the International Logic Programming Symposium, pp. 109\u2013123 (1994)"},{"key":"9386_CR5","unstructured":"Benhamou, F., Goualard, F., Granvilliers, L., Puget, J.-F.: Revising hull and box consistency. In: Proceedings of the International Conference on Logic Programming (ICLP\u201999), pp. 230\u2013244. Las Cruces, USA (1999)"},{"issue":"1","key":"9386_CR6","doi-asserted-by":"crossref","first-page":"138","DOI":"10.1145\/1132973.1132980","volume":"32","author":"L. Granvilliers","year":"2006","unstructured":"Granvilliers L., Benhamou F.: Algorithm 852: RealPaver: an interval solver using constraint satisfaction techniques. ACM Trans. Math. Softw. (TOMS) 32(1), 138\u2013156 (2006)","journal-title":"ACM Trans. Math. Softw. (TOMS)"},{"key":"9386_CR7","doi-asserted-by":"crossref","unstructured":"Hansen, E.R., Walster, G.W.: Global optimization using interval analysis, 2nd edn. Marcel Dekker (2004)","DOI":"10.1201\/9780203026922"},{"issue":"5","key":"9386_CR8","doi-asserted-by":"crossref","first-page":"1038","DOI":"10.1145\/502102.502106","volume":"48","author":"T.J. Hickey","year":"2001","unstructured":"Hickey T.J., Ju Q., Van Emden M.H.: Interval arithmetic: from principles to implementation. J. ACM (JACM) 48(5), 1038\u20131068 (2001)","journal-title":"J. ACM (JACM)"},{"key":"9386_CR9","doi-asserted-by":"crossref","unstructured":"Jaulin, L., Kieffer, M., Didrit, O., Walter, E.: Applied interval analysis, 1st edn. Springer (2001)","DOI":"10.1007\/978-1-4471-0249-6"},{"key":"9386_CR10","unstructured":"Lebbah, Y.: ICOS (Interval Constraints Solver). WWW document (2003)"},{"key":"9386_CR11","unstructured":"Lhomme, O.: Consistency techniques for numeric CSPs. In: Proceedings of the 13th International Joint Conference on Artificial Intelligence (IJCAI-93), pp. 232\u2013238 (1993)"},{"key":"9386_CR12","unstructured":"Lottaz, C.: Collaborative design using solution spaces. PhD thesis, Swiss Federal Institute of Technology in Lausanne (EPFL), Switzerland (2000)"},{"key":"9386_CR13","doi-asserted-by":"crossref","first-page":"99","DOI":"10.1016\/0004-3702(77)90007-8","volume":"8","author":"A.K. Mackworth","year":"1977","unstructured":"Mackworth A.K.: Consistency in networks of relations. Artif. Intell. 8, 99\u2013118 (1977)","journal-title":"Artif. Intell."},{"key":"9386_CR14","doi-asserted-by":"crossref","first-page":"95","DOI":"10.1016\/0020-0255(74)90008-5","volume":"7","author":"U. Montanari","year":"1974","unstructured":"Montanari U.: Networks of constraints: fundamental properties and applications to picture processing. Inf. Sci. 7, 95\u2013132 (1974)","journal-title":"Inf. Sci."},{"key":"9386_CR15","volume-title":"Interval Analysis","author":"R.E. Moore","year":"1966","unstructured":"Moore R.E.: Interval Analysis. Prentice Hall, Englewood Cliffs, NJ (1966)"},{"key":"9386_CR16","doi-asserted-by":"crossref","DOI":"10.1137\/1.9781611970906","volume-title":"Methods and Applications of Interval Analysis","author":"R.E. Moore","year":"1979","unstructured":"Moore R.E.: Methods and Applications of Interval Analysis. SIAM Studies in Applied Mathematics, Philadelphia (1979)"},{"key":"9386_CR17","volume-title":"Interval Methods for Systems of Equations","author":"A. Neumaier","year":"1990","unstructured":"Neumaier A.: Interval Methods for Systems of Equations. Cambridge University Press, Cambridge(1990)"},{"issue":"3","key":"9386_CR18","doi-asserted-by":"crossref","first-page":"251","DOI":"10.1007\/s00607-006-0180-4","volume":"78","author":"J.D. Pryce","year":"2006","unstructured":"Pryce J.D., Corliss G.F.: Interval arithmetic with containment sets. Computing 78(3), 251\u2013276 (2006)","journal-title":"Computing"},{"key":"9386_CR19","unstructured":"Sam-Haroud, D.: Constraint consistency techniques for continuous domains. PhD thesis, Swiss Federal Institute of Technology in Lausanne (EPFL), Switzerland (1995)"},{"key":"9386_CR20","unstructured":"Schichl, H.: Mathematical modeling and global optimization. Habilitation thesis, Faculty of Mathematics, University of Vienna, Autralia, November (2003)"},{"key":"9386_CR21","doi-asserted-by":"crossref","first-page":"541","DOI":"10.1007\/s10898-005-0937-x","volume":"33","author":"H. Schichl","year":"2005","unstructured":"Schichl H., Neumaier A.: Interval analysis on directed acyclic graphs for global optimization. J. Global Optim. 33, 541\u2013562 (2005)","journal-title":"J. Global Optim."},{"key":"9386_CR22","unstructured":"Silaghi, M.-C., Sam-Haroud, D., Faltings, B.: Search techniques for non-linear CSPs with inequalities. In: Proceedings of the 14th Canadian Conference on Artificial Intelligence (2001)"},{"key":"9386_CR23","doi-asserted-by":"crossref","DOI":"10.1007\/978-94-015-8822-5","volume-title":"Fixed point theory and best approximation: the KKM-map principle","author":"S. Singh","year":"1997","unstructured":"Singh S., Watson B., Srivastava P.: Fixed point theory and best approximation: the KKM-map principle. Kluwer Academic Publishers, Dordrecht (1997)"},{"key":"9386_CR24","doi-asserted-by":"crossref","unstructured":"Van Hentenryck, P.: Numerica: a modeling language for global optimization. In: Proceedings of the 15th International Joint Conference on Artificial Intelligence (IJCAI-97) (1997)","DOI":"10.7551\/mitpress\/5073.001.0001"},{"key":"9386_CR25","doi-asserted-by":"crossref","unstructured":"Vu, X.-H., Sam-Haroud, D., Silaghi, M.-C.: Numerical constraint satisfaction problems with non-isolated solutions. In: Global Optimization and Constraint Satisfaction: First International Workshop on Global Constraint Optimization and Constraint Satisfaction, COCOS 2002, LNCS vol. 2861, pp. 194\u2013210. Valbonne-Sophia Antipolis, France, October 2003. Springer-Verlag","DOI":"10.1007\/978-3-540-39901-8_15"},{"key":"9386_CR26","unstructured":"Vu, X.-H., Sam-Haroud, D., Faltings, B.: Combining multiple inclusion representations in numerical constraint propagation. In: Proceedings of the 16th IEEE International Conference on Tools with Artificial Intelligence (ICTAI 2004), pp. 458\u2013467. Florida, USA, November 2004. IEEE Computer Society Press"},{"key":"9386_CR27","doi-asserted-by":"crossref","unstructured":"Vu, X.-H., Schichl, H., Sam-Haroud, D.: Using directed acyclic graphs to coordinate propagation and search for numerical constraint satisfaction problems. In: Proceedings of the 16th IEEE International Conference on Tools with Artificial Intelligence (ICTAI 2004), Florida, USA, November 2004. IEEE Computer Society Press","DOI":"10.1109\/ICTAI.2004.118"},{"key":"9386_CR28","unstructured":"Waltz, D.L.: Generating semantic descriptions from drawings of scenes with shadows. Technical Report, Massachusetts Institute of Technology, USA (1972)"},{"key":"9386_CR29","first-page":"19","volume-title":"The Psychology of Computer Vision, Chapter Understanding Line Drawings of Scenes with Shadows","author":"D.L. Waltz","year":"1975","unstructured":"Waltz D.L.: The Psychology of Computer Vision, Chapter Understanding Line Drawings of Scenes with Shadows, pp. 19\u201391. McGraw Hill, New York (1975)"},{"key":"9386_CR30","unstructured":"William Walster, G., Hansen, E.R., Pryce, J.D.: Extended real intervals and the topological closure of extended real relations. Technical Report, Sun Microsystems, February (2000). http:\/\/wwws.sun.com\/software\/sundev\/whitepapers\/extended-real.pdf"}],"container-title":["Journal of Global Optimization"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10898-008-9386-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10898-008-9386-7\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10898-008-9386-7","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,9,28]],"date-time":"2021-09-28T17:34:38Z","timestamp":1632850478000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10898-008-9386-7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2008,12,24]]},"references-count":30,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2009,12]]}},"alternative-id":["9386"],"URL":"https:\/\/doi.org\/10.1007\/s10898-008-9386-7","relation":{},"ISSN":["0925-5001","1573-2916"],"issn-type":[{"value":"0925-5001","type":"print"},{"value":"1573-2916","type":"electronic"}],"subject":[],"published":{"date-parts":[[2008,12,24]]}}}