{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,5]],"date-time":"2026-01-05T18:37:02Z","timestamp":1767638222156,"version":"3.48.0"},"reference-count":24,"publisher":"Maximum Academic Press","issue":"3","license":[{"start":{"date-parts":[[2010,9,1]],"date-time":"2010-09-01T00:00:00Z","timestamp":1283299200000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["The Knowledge Engineering Review"],"published-print":{"date-parts":[[2010,9]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>\n                    The Simple Temporal Network (STN) is a widely used framework for reasoning about quantitative temporal constraints over variables with continuous or discrete domains. The inference tasks of determining consistency and deriving the minimal network are traditionally achieved by graph algorithms (e.g. Floyd-Warshall, Johnson) or by iteration of narrowing operators (e.g. \u0394STP). None of these methods exploits effectively the tree-decomposition structure of the constraint graph of an STN. Methods based on variable elimination (e.g. adaptive consistency) can exploit this structure, but have not been applied to STNs as far as they could, in part because it is unclear how to efficiently pass the \u2018messages\u2019 over continuous domains. We show that for an STN, these messages can be represented compactly as sub-STNs. We then present an efficient message-passing scheme for computing the minimal constraints of an STN. Analysis of this algorithm,\n                    <jats:italic>Prop-STP<\/jats:italic>\n                    , brings formal explanation of the performance of the existing STN solvers \u0394STP and SR-PC. Empirical results validate the efficiency of Prop-STP, demonstrating performance comparable to \u0394STP, in cases where the constraint graph is known to have small tree width, such as those that arise during Hierarchical Task Network planning.\n                  <\/jats:p>","DOI":"10.1017\/s0269888910000184","type":"journal-article","created":{"date-parts":[[2010,8,23]],"date-time":"2010-08-23T09:25:48Z","timestamp":1282555548000},"page":"337-351","source":"Crossref","is-referenced-by-count":4,"title":["Efficient variable elimination for semi-structured simple temporal networks with continuous domains"],"prefix":"10.48130","volume":"25","author":[{"given":"Neil","family":"Yorke-Smith","sequence":"first","affiliation":[],"role":[{"role":"author","vocab":"crossref"}]},{"given":"Hung H.","family":"Bui","sequence":"additional","affiliation":[],"role":[{"role":"author","vocab":"crossref"}]}],"member":"27968","published-online":{"date-parts":[[2010,9,1]]},"reference":[{"key":"S0269888910000184_ref22","doi-asserted-by":"publisher","DOI":"10.1017\/S0269888900001089"},{"key":"S0269888910000184_ref9","doi-asserted-by":"publisher","DOI":"10.1016\/0004-3702(91)90006-6"},{"key":"S0269888910000184_ref12","doi-asserted-by":"crossref","unstructured":"Hunsberger L. 2008. A practical temporal constraint management system for real-time applications. In Proceedings of ECAI\u201908, Patras, Greece.","DOI":"10.3233\/978-1-58603-891-5-553"},{"key":"S0269888910000184_ref19","unstructured":"Myers K. L. , Tyson M. W. , Wolverton M. J. , Jarvis P. A. , Lee T. J. , desJardins M. 2002. PASSAT: a user-centric planning framework. In Proceedings of the Third Intl. NASA Workshop on Planning and Scheduling for Space, Houston, TX."},{"key":"S0269888910000184_ref20","unstructured":"Planken L. , de Weerdt M. , van der Krogt R. 2008. P3C: a new algorithm for the simple temporal problem. In Proceedings of ICAPS\u201908, Sydney, Australia."},{"key":"S0269888910000184_ref21","unstructured":"Shi Y. , Lal A. , Choueiry B. Y. 2004. Evaluating consistency algorithms for temporal metric constraints. In Proceedings of AAAI-04, San Jose, CA."},{"key":"S0269888910000184_ref24","unstructured":"Yorke-Smith N. 2005. Exploiting the structure of hierarchical plans in temporal constraint propagation. In Proceedings of AAAI-05, Pittsburgh, PA."},{"volume-title":"Introduction to Algorithms","year":"1990","author":"Cormen","key":"S0269888910000184_ref7"},{"key":"S0269888910000184_ref6","unstructured":"Choueiry B. Y. , Wilson N. 2006. Personal communication."},{"key":"S0269888910000184_ref10","doi-asserted-by":"publisher","DOI":"10.1016\/0004-3702(89)90037-4"},{"key":"S0269888910000184_ref15","unstructured":"Khatib L. , Morris P. , Morris R. A. , Rossi F. 2001. Temporal constraint reasoning with preferences. In Proceedings of IJCAI\u201901, Seattle, WA."},{"volume-title":"Constraint Processing","year":"2003","author":"Dechter","key":"S0269888910000184_ref8"},{"key":"S0269888910000184_ref23","unstructured":"Xu L. , Choueiry B. Y. 2003. A new efficient algorithm for solving the simple temporal problem. In Proceedings of TIME\u201903, Cairns, Australia."},{"key":"S0269888910000184_ref18","doi-asserted-by":"crossref","first-page":"421","DOI":"10.1613\/jair.1541","article-title":"On the practical use of variable elimination in constraint optimization problems: \u2018still-life\u2019 as a case study","volume":"23","author":"Larrosa","year":"2005","journal-title":"Journal of Artificial Intelligence Research"},{"key":"S0269888910000184_ref13","doi-asserted-by":"crossref","unstructured":"J\u00e9gou P. , Ndiaye S. , Terrioux C. 2005. Computing and exploiting tree-decompositions for solving constraint networks. In Proceedings of CP\u201905, Sitges, Spain.","DOI":"10.1007\/11564751_63"},{"key":"S0269888910000184_ref1","unstructured":"Bliek C. , Sam-Haroud D. 1999. Path consistency on triangulated constraint graphs. In Proceedings of IJCAI\u201999, Stockholm, Sweden."},{"key":"S0269888910000184_ref2","unstructured":"Bresina J. , J\u00f3nsson A. K. , Morris P. , Rajan K. 2005. Activity planning for the Mars exploration rovers. In Proceedings of ICAPS\u201905, Monterey, CA."},{"key":"S0269888910000184_ref14","doi-asserted-by":"publisher","DOI":"10.1016\/S0004-3702(02)00400-9"},{"volume-title":"Semantics for Hierarchical Task-network Planning","year":"1994","author":"Erol","key":"S0269888910000184_ref11"},{"key":"S0269888910000184_ref5","doi-asserted-by":"crossref","unstructured":"Castillo L. , Fdez-Olivares J. , Garc\u00eda-P\u00e9rez F. P. O. 2006. Efficiently handling temporal knowledge in an HTN planner. In Proceedings of ICAPS\u201906, Cumbria, UK.","DOI":"10.1007\/11881216_45"},{"key":"S0269888910000184_ref17","unstructured":"Laborie P. , Ghallab M. 1995. Planning with sharable resource constraints. In Proceedings of IJCAI\u201995, Montr\u00e9al, Canada."},{"volume-title":"Triangulation of Graphs: Algorithms Giving Small Total State Space","year":"1990","author":"Kjaerulff","key":"S0269888910000184_ref16"},{"key":"S0269888910000184_ref3","unstructured":"Bui H. H. , Tyson M. , Yorke-Smith N. 2007. Efficient message passing and propagation of simple temporal constraints. In Proceedings of AAAI 2007 Workshop on Spatial and Temporal Reasoning, Vancouver, Canada."},{"key":"S0269888910000184_ref4","unstructured":"Bui H. H. , Tyson M. , Yorke-Smith N. 2008. Efficient message passing and propagation of simple temporal constraints: Results on semi-structured networks. In Proceedings of CP\/ICAPS\u201908 Workshop on Constraint Satisfaction for Planning and Scheduling Problems, Sydney, Australia."}],"container-title":["The Knowledge Engineering Review"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0269888910000184","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,1,5]],"date-time":"2026-01-05T14:43:57Z","timestamp":1767624237000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0269888910000184\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,9]]},"references-count":24,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2010,9]]}},"alternative-id":["S0269888910000184"],"URL":"https:\/\/doi.org\/10.1017\/s0269888910000184","relation":{},"ISSN":["0269-8889","1469-8005"],"issn-type":[{"type":"print","value":"0269-8889"},{"type":"electronic","value":"1469-8005"}],"subject":[],"published":{"date-parts":[[2010,9]]}}}