Abstract
In commercial network database management systems, set-valued fields and aggregate functions are commonly supported. However, the relational database model, as defined by Codd, does not include set-valued attributes or aggregate functions. Recently, Klug extended the relational model by incorporating aggregate functions and by defining relational algebra and calculus languages.
In this paper, relational algebra and relational calculus database query languages (as defined by Klug) are extended to manipulate set-valued attributes and to utilize aggregate functions. The expressive power of the extended languages is shown to be equivalent. We extend the relational algebra with three new operators, namely, pack, unpack, and aggregation-by-template. The extended languages form a theoretical framework for statistical database query languages.
- 1 ABITEBOUL, S., AND BIDOIT, N. Non first normal form relations to represent hierarchically organized data. in Proceedings of the 3rd ACM SIGACT-~IGMOD Symposium on Principles of Database Systems (Waterloo, Ont., Apr. 2-4, 1984), ACM, New York, 1984. Google ScholarDigital Library
- 2 CHAMBERLIN, D. D. ET AL. SEQUEL 2: a unified approach to data definition, manipulation and control. Lz~ ~. aes. Dev. 20, 6 (~oy, oou-o ~o.Google Scholar
- 3 CODD, E.F. Relational completeness of database sublanguages. In Data Base Systems. Courant Computer Science Symposium 6, R. Rustin, Ed. Prentice-Hall, Englewood Cliffs, N.J., 1971.Google Scholar
- 4 DATTA, A. Implementation and peroformance analysis of STBE. Master's thesis, Dept. of Computer Engineering and Science, Case Western Reserve Univ., Cleveland, Oh., 1985.Google Scholar
- 5 FXSCHER, P., AND THOMAS, S. Operators for non-first-normal-form relations. In Proceedings ofGoogle Scholar
- 6 FOURN}ER B. A display manager for STBE. Master's Thesis, Dept. of Computer Engineering and Science, Case Western Reserve Univ., Cleveland, Oh., Sept. 1985.Google Scholar
- 7 Hou, W-C. The implementation of the extended relational database management system. Master's Thesis, Dept. of Computer Engineering and Science, Case Western Reserve Univ., Cleveland, Oh., Jan. 1985.Google Scholar
- 8 JAcoBs, B.E. On database logic. J. ACM 29, 2 (Apr. 1982), 310-332. Google ScholarDigital Library
- 9 JAESCHKE, G., AND SCHEK, H.J. Remarks on the algebra of nonfirst normal form relations. In Proceedings of the 1st A CM SIGACT/SIGMOD Symposium on Principles of Database Systems (Los Angeles, Calif., Mar. 29-31, 1982). ACM, New York, 1982. Google ScholarDigital Library
- 10 KLUG, A. Abe~A query language for constructing aggregates-by-example, in Proceedings of the 1st International Workshop on Statistical Database Management {Menlo Park, Calif., Dec. 2-4, 1981). Lawrence Berkeley Labs., Univ. of California, Berkeley, 1981, 190-206. Google ScholarDigital Library
- 11 KLU~, A. Equivalence of relational algebra and relational calculus query languages having aggregate functions. J. ACM 29, 3 (July 1982), 699-717. Google ScholarDigital Library
- 12 KLU(~, A. Access paths in the Abe statistical query facility. In Proceedings of A CM SIGMOD Conference (1982). ACM, New York, 1982. Google ScholarDigital Library
- 13 MCCARTHY (ED.) Proceedings, 2nd International Workshop on Statistical Database Management Lawrence Berkeley Labs., Univ. of California, Berkeley, 1983.Google Scholar
- 14 ORMAN, L. Semantics of indexed sets. Cornell University WorIring Paper, 198!:Google Scholar
- 15 ORMAN, L. Nested set languages for functional databases. Inf. Syst. 9, 3/4 (1984), 241-249. Google ScholarDigital Library
- 16 0zsoYoSLU, G., AND MATOS, V. On optimizing summary-table-by example queries. In Proceedings Of the ACM-SIGMOD International Conference (Austin, Tex., May 28-31, 1985). ACM, New York, 1985. Google ScholarDigital Library
- 17 OZSOYOG,LU, G., AND OZSOYOg~LU, Z. M. Features of a system for statistical databases. In Proceedings of the 2nd International Workshop on Statistical Database Management (Los Altos, Calif., Sept. 27-29, 1983). Lawrence Berkeley Labs., Univ. of California, Berkeley, 1983, 9-18. Google ScholarDigital Library
- 18 0ZSO~O(~LU, Z. M., AND 0ZSOYOSLU, G. An extension of relational algebra for summary tables. In Proceedings of the 2nd international Workshop on Statistical Database Management (Los Altos, UaUL, Sept. 27-29, i983). Lawrence Berkeley Labs., Univ. ot ual~tornia, Berkeley, ~:t, 202-212. Google ScholarDigital Library
- 19 0ZSOYOSLU, Z. M., AND 0ZSOYO~,LU, G. STBE~A database query language for manipulating summary data. In Proceedings of the IEEE COMPDEC Conference (Chicago, Nov. 1984), IEEE, New York, 1984. Google ScholarDigital Library
- 20 OZOYOGLU, Z.M. AND OZSOYOGLU, G. A query language for statistical databses. InQuery Processing in Database Systems, W. Kim, D. Reiner, D. Batory, Eds. Springer-Verlag, New York, 1984.Google Scholar
- 21 6ZSOYO(~LU, G., (SZSOYO(~LU, Z. M., AND MATA, F. A lanmmge and a physical o~anization technique for summary tables. In Proceedings of the 4th A CM SIGACT/SIGMOD Symposium on Principles of Database Systems (Austin, Tex., May 28-31, 1985). ACM, New York, 1985. Google ScholarDigital Library
- 22 0ZSOYO(~LU, Z. M., AND YUAN, L.-Y. A normal form for nested relations, in Proceedings of the 4th ACM SIGACT/SIGMOD Symposium on Principles of Database Systems (Austin, Tex., May 28-31, 1985). ACM, New York, 1985. Google ScholarDigital Library
- 22a 0ZSOYO(~LU, G., AND WONG, H.-Q. A relational calculus with set operators, its safety, and equivalent graphical languages. Tech. Rep., Dept. Computer Engineering and Science, Case Western Reserve Univ., Cleveland, Oh., 1987.Google Scholar
- 23 SOFTWARE, AG. ADABAS Reference Manual. Software AG of North America, Reston, Va., 1981.Google Scholar
- 24 ROTH, M. A., KORTH, H. F., AND SILBERSCHATZ, A. Theory of non-first-normal-form relational databases. Tech. Rep., Univ. of Texas at Austin, 1985.Google Scholar
- 25 STONEBRAKER, M., WONG, E., KREPS, r., AND HELD, G. The design and implementation of INGRES. ACM Trans. Database Syst. 1, 3 (1976), 189-222. Google ScholarDigital Library
- 26 H. K. WONG, (ED.) Proceedings, 1st International Workshop on Statistical Database Manage-Google Scholar
Index Terms
Extending relational algebra and relational calculus with set-valued attributes and aggregate functions
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