{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,29]],"date-time":"2026-09-29T11:47:24Z","timestamp":1790682444210,"version":"4.1.0"},"reference-count":25,"publisher":"Association for Computing Machinery (ACM)","issue":"2","license":[{"start":{"date-parts":[[2011,5,1]],"date-time":"2011-05-01T00:00:00Z","timestamp":1304208000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"funder":[{"DOI":"10.13039\/100000145","name":"Division of Information and Intelligent Systems","doi-asserted-by":"publisher","award":["IIS-0905276IIS-0905276"],"award-info":[{"award-number":["IIS-0905276IIS-0905276"]}],"id":[{"id":"10.13039\/100000145","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000145","name":"Division of Information and Intelligent Systems","doi-asserted-by":"publisher","award":["IIS-0347065"],"award-info":[{"award-number":["IIS-0347065"]}],"id":[{"id":"10.13039\/100000145","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Database Syst."],"published-print":{"date-parts":[[2011,5]]},"abstract":"<jats:p>\n            An inverse of a schema mapping\n            <jats:italic>M<\/jats:italic>\n            is intended to undo what\n            <jats:italic>M<\/jats:italic>\n            does, thus providing a way to perform reverse data exchange. In recent years, three different formalizations of this concept have been introduced and studied, namely the notions of an inverse of a schema mapping, a quasi-inverse of a schema mapping, and a maximum recovery of a schema mapping. The study of these notions has been carried out in the context in which source instances are restricted to consist entirely of constants, while target instances may contain both constants and labeled nulls. This restriction on source instances is crucial for obtaining some of the main technical results about these three notions, but, at the same time, limits their usefulness, since reverse data exchange naturally leads to source instances that may contain both constants and labeled nulls.\n          <\/jats:p>\n          <jats:p>We develop a new framework for reverse data exchange that supports source instances that may contain nulls, and we thereby overcome the semantic mismatch between source and target instances of the previous formalizations. The development of this new framework requires a careful reformulation of all the important notions, including the notions of the identity schema mapping, inverse, and maximum recovery. To this effect, we introduce the notions of extended identity schema mapping, extended inverse, and maximum extended recovery, by making systematic use of the homomorphism relation on instances. We give results concerning the existence of extended inverses and of maximum extended recoveries, and results concerning their applications to reverse data exchange and query answering. Moreover, we show that maximum extended recoveries can be used to capture in a quantitative way, the amount of information loss embodied in a schema mapping specified by source-to-target tuple-generating dependencies.<\/jats:p>","DOI":"10.1145\/1966385.1966389","type":"journal-article","created":{"date-parts":[[2011,6,6]],"date-time":"2011-06-06T11:51:38Z","timestamp":1307361098000},"page":"1-42","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":13,"title":["Reverse data exchange"],"prefix":"10.1145","volume":"36","author":[{"given":"Ronald","family":"Fagin","sequence":"first","affiliation":[{"name":"IBM Research - Almaden"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Phokion G.","family":"Kolaitis","sequence":"additional","affiliation":[{"name":"UC Santa Cruz and IBM Research - Almaden"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Lucian","family":"Popa","sequence":"additional","affiliation":[{"name":"IBM Research - Almaden"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Wang-Chiew","family":"Tan","sequence":"additional","affiliation":[{"name":"IBM Research - Almaden and UC Santa Cruz"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"320","published-online":{"date-parts":[[2011,6,2]]},"reference":[{"key":"e_1_2_1_1_1","unstructured":"Abiteboul S. Hull R. and Vianu V. 1995. Foundations of Databases. Addison-Wesley.   Abiteboul S. Hull R. and Vianu V. 1995. Foundations of Databases. Addison-Wesley."},{"key":"e_1_2_1_2_1","volume-title":"Proceedings of the International ICST Conference on Scalable Information Systems (InfoScale).","author":"Afrati F.","unstructured":"Afrati , F. , Li , C. , and Pavlaki , V . 2008. Data exchange: Query answering on incomplete data sources . In Proceedings of the International ICST Conference on Scalable Information Systems (InfoScale). Afrati, F., Li, C., and Pavlaki, V. 2008. Data exchange: Query answering on incomplete data sources. In Proceedings of the International ICST Conference on Scalable Information Systems (InfoScale)."},{"key":"e_1_2_1_3_1","doi-asserted-by":"publisher","DOI":"10.1145\/1815933.1815938"},{"key":"e_1_2_1_4_1","volume-title":"Proceedings of the International Conference on Very Large Data Bases (VLDB). 1018--1029","author":"Arenas M.","unstructured":"Arenas , M. , P\u00e9rez , J. , Reutter , J. L. , and Riveros , C . 2009b. Inverting schema mappings: Bridging the gap between theory and practice . In Proceedings of the International Conference on Very Large Data Bases (VLDB). 1018--1029 . Arenas, M., P\u00e9rez, J., Reutter, J. L., and Riveros, C. 2009b. Inverting schema mappings: Bridging the gap between theory and practice. In Proceedings of the International Conference on Very Large Data Bases (VLDB). 1018--1029."},{"key":"e_1_2_1_5_1","doi-asserted-by":"publisher","DOI":"10.1145\/1807085.1807116"},{"key":"e_1_2_1_6_1","doi-asserted-by":"publisher","DOI":"10.1145\/1620585.1620589"},{"key":"e_1_2_1_7_1","doi-asserted-by":"publisher","DOI":"10.1145\/1634.1636"},{"key":"e_1_2_1_8_1","volume-title":"Proceedings of the Conference on Innovative Data Systems Research (CIDR). 209--220","author":"Bernstein P. A.","year":"2003","unstructured":"Bernstein , P. A. 2003 . Applying model management to classical meta-data problems . In Proceedings of the Conference on Innovative Data Systems Research (CIDR). 209--220 . Bernstein, P. A. 2003. Applying model management to classical meta-data problems. In Proceedings of the Conference on Innovative Data Systems Research (CIDR). 209--220."},{"key":"e_1_2_1_9_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00778-007-0059-9"},{"key":"e_1_2_1_10_1","volume-title":"Proceedings of the International Workshop on Database Programming Languages (DBPL). 21--39","author":"Deutsch A.","unstructured":"Deutsch , A. and Tannen , V . 2001. Optimization properties for classes of conjunctive regular path queries . In Proceedings of the International Workshop on Database Programming Languages (DBPL). 21--39 . Deutsch, A. and Tannen, V. 2001. Optimization properties for classes of conjunctive regular path queries. In Proceedings of the International Workshop on Database Programming Languages (DBPL). 21--39."},{"key":"e_1_2_1_11_1","doi-asserted-by":"publisher","DOI":"10.1145\/1292609.1292615"},{"key":"e_1_2_1_12_1","doi-asserted-by":"publisher","DOI":"10.1O16\/j.tcs.2004.10.033"},{"key":"e_1_2_1_13_1","doi-asserted-by":"publisher","DOI":"10.1145\/1114244.1114249"},{"key":"e_1_2_1_14_1","doi-asserted-by":"publisher","DOI":"10.1145\/1366102.1366108"},{"key":"e_1_2_1_15_1","doi-asserted-by":"publisher","DOI":"10.1145\/1559795.1559800"},{"key":"e_1_2_1_16_1","volume-title":"-C","author":"Fagin R.","year":"2011","unstructured":"Fagin , R. , Kolaitis , P. G. , Popa , L. , and Tan , W . -C . 2011 . Schema mapping evolution through composition and inversion. In Schema Matching and Mapping, Z. Bellahsene and A. Bonifati and E. Rahm, Ed. Springer , 191--222. Fagin, R., Kolaitis, P. G., Popa, L., and Tan, W.-C. 2011. Schema mapping evolution through composition and inversion. In Schema Matching and Mapping, Z. Bellahsene and A. Bonifati and E. Rahm, Ed. Springer, 191--222."},{"key":"e_1_2_1_17_1","doi-asserted-by":"publisher","DOI":"10.1145\/1857914.1857915"},{"key":"e_1_2_1_18_1","volume-title":"Proceedings of the International Conference on Very Large Data Bases (VLDB). 67--78","author":"Fuxman A.","unstructured":"Fuxman , A. , Hern\u00e1ndez , M. A. , Ho , C. T. H. , Miller , R. J. , Papotti , P. , and Popa , L . 2006. Nested mappings: Schema mapping reloaded . In Proceedings of the International Conference on Very Large Data Bases (VLDB). 67--78 . Fuxman, A., Hern\u00e1ndez, M. A., Ho, C. T. H., Miller, R. J., Papotti, P., and Popa, L. 2006. Nested mappings: Schema mapping reloaded. In Proceedings of the International Conference on Very Large Data Bases (VLDB). 67--78."},{"key":"e_1_2_1_19_1","doi-asserted-by":"publisher","DOI":"10.1145\/582192.582222"},{"key":"e_1_2_1_20_1","doi-asserted-by":"publisher","DOI":"10.1145\/1634.1886"},{"key":"e_1_2_1_21_1","doi-asserted-by":"publisher","DOI":"10.1145\/543613.543644"},{"key":"e_1_2_1_22_1","volume-title":"Proceedings of the International Conference on Very Large Data Bases (VLDB). 572--583","author":"Madhavan J.","unstructured":"Madhavan , J. and Halevy , A. Y . 2003. Composing mappings among data sources . In Proceedings of the International Conference on Very Large Data Bases (VLDB). 572--583 . Madhavan, J. and Halevy, A. Y. 2003. Composing mappings among data sources. In Proceedings of the International Conference on Very Large Data Bases (VLDB). 572--583."},{"key":"e_1_2_1_23_1","series-title":"Lecture Notes in Computer Science","volume-title":"Generic Model Management: Concepts and Algorithms","author":"Melnik S.","unstructured":"Melnik , S. 2004. Generic Model Management: Concepts and Algorithms . Lecture Notes in Computer Science , vol. 2967 , Springer . Melnik, S. 2004. Generic Model Management: Concepts and Algorithms. Lecture Notes in Computer Science, vol. 2967, Springer."},{"key":"e_1_2_1_24_1","doi-asserted-by":"publisher","DOI":"10.1145\/1065167.1065189"},{"key":"e_1_2_1_25_1","volume-title":"Proceedings of the International Conference on Very Large Data Bases (VLDB). 598--609","author":"Popa L.","unstructured":"Popa , L. , Velegrakis , Y. , Miller , R. J. , Hern\u00e1ndez , M. A. , and Fagin , R . 2002. Translating Web data . In Proceedings of the International Conference on Very Large Data Bases (VLDB). 598--609 . Popa, L., Velegrakis, Y., Miller, R. J., Hern\u00e1ndez, M. A., and Fagin, R. 2002. Translating Web data. In Proceedings of the International Conference on Very Large Data Bases (VLDB). 598--609."}],"container-title":["ACM Transactions on Database Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/1966385.1966389","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/1966385.1966389","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T11:22:26Z","timestamp":1750245746000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/1966385.1966389"}},"subtitle":["Coping with nulls"],"short-title":[],"issued":{"date-parts":[[2011,5]]},"references-count":25,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2011,5]]}},"alternative-id":["10.1145\/1966385.1966389"],"URL":"https:\/\/doi.org\/10.1145\/1966385.1966389","relation":{},"ISSN":["0362-5915","1557-4644"],"issn-type":[{"value":"0362-5915","type":"print"},{"value":"1557-4644","type":"electronic"}],"subject":[],"published":{"date-parts":[[2011,5]]},"assertion":[{"value":"2009-10-01","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2011-02-01","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2011-06-02","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}