{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,14]],"date-time":"2026-05-14T04:46:31Z","timestamp":1778733991094,"version":"3.51.4"},"reference-count":22,"publisher":"Association for Computing Machinery (ACM)","issue":"3","license":[{"start":{"date-parts":[[2005,9,1]],"date-time":"2005-09-01T00:00:00Z","timestamp":1125532800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Database Syst."],"published-print":{"date-parts":[[2005,9]]},"abstract":"<jats:p>\n            In multidimensional data models intended for online analytic processing (OLAP), data are viewed as points in a multidimensional space. Each dimension has structure, described by a directed graph of categories, a set of members for each category, and a child\/parent relation between members. An important application of this structure is to use it to infer summarizability, that is, whether an aggregate view defined for some category can be correctly derived from a set of precomputed views defined for other categories. A dimension is called\n            <jats:italic>structurally heterogeneous<\/jats:italic>\n            if two members in a given category are allowed to have ancestors in different categories. In this article, we propose a class of integrity constraints,\n            <jats:italic>dimension constraints<\/jats:italic>\n            , that allow us to reason about summarizability in heterogeneous dimensions. We introduce the notion of frozen dimensions which are minimal homogeneous dimension instances representing the different structures that are implicitly combined in a heterogeneous dimension. Frozen dimensions provide the basis for efficiently testing the implication of dimension constraints and are a useful aid to understanding heterogeneous dimensions. We give a sound and complete algorithm for solving the implication of dimension constraints that uses heuristics based on the structure of the dimension and the constraints to speed up its execution. We study the intrinsic complexity of the implication problem and the running time of our algorithm.\n          <\/jats:p>","DOI":"10.1145\/1093382.1093388","type":"journal-article","created":{"date-parts":[[2005,11,7]],"date-time":"2005-11-07T16:00:45Z","timestamp":1131379245000},"page":"854-886","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":53,"title":["Capturing summarizability with integrity constraints in OLAP"],"prefix":"10.1145","volume":"30","author":[{"given":"Carlos A.","family":"Hurtado","sequence":"first","affiliation":[{"name":"Universidad de Chile, Chile, C. P"}]},{"given":"Claudio","family":"Gutierrez","sequence":"additional","affiliation":[{"name":"Universidad de Chile, Chile, C. P"}]},{"given":"Alberto O.","family":"Mendelzon","sequence":"additional","affiliation":[{"name":"University of Toronto"}]}],"member":"320","published-online":{"date-parts":[[2005,9]]},"reference":[{"key":"e_1_2_2_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_2_2_1","doi-asserted-by":"publisher","DOI":"10.1006\/jcss.1999.1627"},{"key":"e_1_2_2_3_1","volume-title":"Proceedings of 22th International Conference on Very Large Data Bases (VLDB'96)","author":"Agarwal S.","unstructured":"Agarwal , S. , Agrawal , R. , Deshpande , P. , Gupta , A. , Naughton , J. F. , Ramakrishnan , R. , and Sarawagi , S . 1996. On the computation of multidimensional aggregates . In Proceedings of 22th International Conference on Very Large Data Bases (VLDB'96) . Mumbai (Bombay), India. 506--521.]] Agarwal, S., Agrawal, R., Deshpande, P., Gupta, A., Naughton, J. F., Ramakrishnan, R., and Sarawagi, S. 1996. On the computation of multidimensional aggregates. In Proceedings of 22th International Conference on Very Large Data Bases (VLDB'96). Mumbai (Bombay), India. 506--521.]]"},{"key":"e_1_2_2_4_1","doi-asserted-by":"crossref","unstructured":"Borger E. Gradel E. and Gurevich Y. 1996. The Classical Decision Problem. Springer Berlin Germany.]]  Borger E. Gradel E. and Gurevich Y. 1996. The Classical Decision Problem. Springer Berlin Germany.]]","DOI":"10.1007\/978-3-642-59207-2_1"},{"key":"e_1_2_2_5_1","doi-asserted-by":"publisher","DOI":"10.1145\/275487.275502"},{"key":"e_1_2_2_6_1","volume-title":"Proceedings of the 6th International Workshop on Database Programming Languages (DBLP-6)","author":"Cabibbo L.","unstructured":"Cabibbo , L. and Torlone , R . 1998. Querying multidimensional databases . In Proceedings of the 6th International Workshop on Database Programming Languages (DBLP-6) . London, UK. 319--335.]] Cabibbo, L. and Torlone, R. 1998. Querying multidimensional databases. In Proceedings of the 6th International Workshop on Database Programming Languages (DBLP-6). London, UK. 319--335.]]"},{"key":"e_1_2_2_7_1","volume-title":"Proceedings of the IEEE 7th International Conference on Very Large Data Bases","author":"Goldstein B. S.","year":"1981","unstructured":"Goldstein , B. S. 1981 . Constraints on null values in relational databases . In Proceedings of the IEEE 7th International Conference on Very Large Data Bases . Cannes, France. 101--110.]] Goldstein, B. S. 1981. Constraints on null values in relational databases. In Proceedings of the IEEE 7th International Conference on Very Large Data Bases. 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Generalized projections: A powerful approach to aggregation . In Proceedings of the 21st International Conference on Very Large Data Bases . Zurich, Switzerland. 193--200.]] Gupta, A., Harinarayan, V., and Quass, D. 1995. Generalized projections: A powerful approach to aggregation. In Proceedings of the 21st International Conference on Very Large Data Bases. Zurich, Switzerland. 193--200.]]"},{"key":"e_1_2_2_10_1","volume-title":"Proceedings of the 3rd International Symposium on Foundations of Information and Knowledge Systems","author":"Hurtado C.","unstructured":"Hurtado , C. and Gutierrez , C . 2004. Equivalence of OLAP dimension schemas . In Proceedings of the 3rd International Symposium on Foundations of Information and Knowledge Systems . Wilhelminenburg Castle, Austria. 176--195.]] Hurtado, C. and Gutierrez, C. 2004. Equivalence of OLAP dimension schemas. In Proceedings of the 3rd International Symposium on Foundations of Information and Knowledge Systems. Wilhelminenburg Castle, Austria. 176--195.]]"},{"key":"e_1_2_2_11_1","unstructured":"Hurtado C. Gutierrez C. and Mendelzon A. 2003. Capturing summarizability with integrity constraint in OLAP. Tech. rep. TR\/DCC-2003-6 Department of Computer Science Universidad de Chile.]]  Hurtado C. Gutierrez C. and Mendelzon A. 2003. Capturing summarizability with integrity constraint in OLAP. Tech. rep. TR\/DCC-2003-6 Department of Computer Science Universidad de Chile.]]"},{"key":"e_1_2_2_12_1","volume-title":"Proceedings of the 8th International Conference on Database Theory","author":"Hurtado C.","unstructured":"Hurtado , C. and Mendelzon , A . 2001. Reasoning about summarizability in heterogeneous multidimensional schemas . In Proceedings of the 8th International Conference on Database Theory . London, UK. 375--389.]] Hurtado, C. and Mendelzon, A. 2001. Reasoning about summarizability in heterogeneous multidimensional schemas. 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