A recursive algebra for nested relations

Abstract The nested relational model provides a better representational model for complex objects than the (flat) relational model by allowing relations to have relation-valued attributes. A recursive algebra for nested relations that allows relations to be accessed and modified at all levels without always having to flatten them is presented in this paper. The operators of the classical nested relational algebra are extended with recursive definitions so that they can be applied not only to relations but also to subrelations of a relation. Queries are much more efficient and succinct when expressed in this algebra than in languages that require restructuring in order to access subrelations of relations. A sketch of a proof showing the equivalence of the expressive powers of the recursive algebra and the nested relational algebra is given.

[1]  Per-Åke Larson,et al.  An algebra for nested relations , 1987 .

[2]  Volker Linnemann.  Non first normal form relations and recursive queries: An SQL-based approach , 1987, 1987 IEEE Third International Conference on Data Engineering.

[3]  Peter Dadam,et al.  A DBMS prototype to support extended NF2 relations: an integrated view on flat tables and hierarchies , 1986, SIGMOD '86.

[4]  Serge Abiteboul,et al.  Non first normal form relations to represent hierarchically organized data , 1984, PODS.

[5]  Patrick C. Fischer,et al.  Nested Relational Structures , 1986, Adv. Comput. Res..

[6]  Hans-Jörg Schek,et al.  The relational model with relation-valued attributes , 1986, Inf. Syst..

[7]  Peter Pistor,et al.  Designing A Generalized NF2 Model with an SQL-Type Language Interface , 1986, VLDB.

[8]  Gultekin Özsoyoglu,et al.  Extending relational algebra and relational calculus with set-valued attributes and aggregate functions , 1987, TODS.

[9]  Hans-Jörg Schek,et al.  A Storage System for Complex Objects , 1986, OODBS.

[10]  Michel Scholl,et al.  On Line Processing of Compacted Relations , 1982, VLDB.

[11]  Akifumi Makinouchi,et al.  A Consideration on Normal Form of Not-Necessarily-Normalized Relation in the Relational Data Model , 1977, VLDB.

[12]  P Pistor,et al.  A database language for sets, lists and tables , 1986, Inf. Syst..

[13]  Hans-Jörg Schek,et al.  Architecture and implementation of the Darmstadt database kernel system , 1987, SIGMOD '87.

[14]  Marc Gyssens,et al.  The powerset algebra as a result of adding programming constructs to the nested relational algebra , 1988, SIGMOD '88.

[15]  Dirk Van Gucht,et al.  On the expressive power of the extended relational algebra for the unnormalized relational model , 1987, PODS.

[16]  Latha S. Colby.  A recursive algebra and query optimization for nested relations , 1989, SIGMOD '89.

[17]  Abraham Silberschatz,et al.  Extended algebra and calculus for nested relational databases , 1988, TODS.

[18]  Henry F. Korth,et al.  SQL/NF: a query language for ¬1 NF relational databases , 1987, Inf. Syst..

[19]  Hans-Jörg Schek,et al.  Remarks on the algebra of non first normal form relations , 1982, PODS.

[20]  Patrick C. Fischer,et al.  Multilevel Nested Relational Structures , 1988, J. Comput. Syst. Sci..

[21]  E. F. Codd,et al.  A relational model of data for large shared data banks , 1970, CACM.

[22]  Hans-Jörg Schek,et al.  Supporting Flat Relations by a Nested Relational Kernel , 1987, VLDB.