Association Algebra: A Mathematical Foundation for Object-Oriented Databases.

Stanley Y. W. Su, Mingsen Guo, Herman Lam: Association Algebra: A Mathematical Foundation for Object-Oriented Databases. IEEE Trans. Knowl. Data Eng. 5(5): 775-798(1993)
  author    = {Stanley Y. W. Su and
               Mingsen Guo and
               Herman Lam},
  title     = {Association Algebra: A Mathematical Foundation for Object-Oriented
  journal   = {IEEE Trans. Knowl. Data Eng.},
  volume    = {5},
  number    = {5},
  year      = {1993},
  pages     = {775-798},
  ee        = {db/journals/tkde/SuGL93.html},
  bibsource = {DBLP,}


The application of the object-oriented (O-O) paradigm in the database management field has gained much attention in recent years. Several experimental and commercial O-O database management systems have become available; however, the existing O-O DBMS's still lack a solid mathematical foundation for the manipulation of O-O databases, the optimization of queries, and the design and selection of storage structures for supporting O-O database manipulations. This paper presents an association algebra (A-algebra) to serve as a mathematical foundation for processing O-O databases, which is analogous to the relational algebra used for processing relational databases. In this algebra, objects and their associations in an O-O database are uniformly represented by association patterns which are manipulated by a number of operators to produce other association patterns. Different from the relational algebra, in which set operations operate on relations with union-compatible structures, the A-algebra operators can operate on association patterns of homogeneous and heterogeneous structures. Different from the traditional record-based relational processing, the A-algebra allows very complex patterns of object associations to be directly manipulated. In this paper, the pattern-based query formulation and the A-algebra operators are described. Some mathematical properties of the algebraic operators are presented together with their application in query decomposition and optimization. The completeness of the A-algebra is also defined and proven. The A-algebra has been used as the basis for the design and implementation of an object-oriented query language, OQL, which is the query language used in a prototype Knowledge Base Management System OSAM*.KBMS.

Copyright © 1993 by The Institute of Electrical and Electronic Engineers, Inc. (IEEE). Abstract used with permission.

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A. M. Alashqur, Stanley Y. W. Su, Herman Lam: OQL: A Query Language for Manipulating Object-oriented Databases. VLDB 1989: 433-442 BibTeX
A. M. Alashqur, Stanley Y. W. Su, Herman Lam: A Rule-based Language for Deductive Object-Oriented Databases. ICDE 1990: 58-67 BibTeX
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Referenced by

  1. Stanley Y. W. Su, Soon J. Hyun, Hsin-Hsing M. Chen: Temporal Association Algebra: A Mathematical Foundation for Processing Object-Oriented Temporal Databases. IEEE Trans. Knowl. Data Eng. 10(3): 389-408(1998)
  2. George Semeczko, Stanley Y. W. Su, Tsae-Feng Yu, Fang Wang: Supporting Distributed Query Processing in a Heterogeneous Environment. DASFAA 1997: 107-116
  3. George Semeczko, Stanley Y. W. Su: Supporting Object Migration in Distributed Systems. DASFAA 1997: 59-66
  4. Carlos A. Tau, Clara Smith, Claudia Pons, Ana María Monteiro: Formally Speaking About Schemata, Bases, Classes and Objects. DASFAA 1995: 308-317
  5. Nabil Kamel, Ping Wu, Stanley Y. W. Su: A Pattern-Based Object Calculus. VLDB J. 3(1): 53-76(1994)
  6. Stanley Y. W. Su, Herman Lam, Srinivasa Eddula, Javier Arroyo, Neeta Prasad, Ronghao Zhuang: OSAM*KBMS: An Object-Oriented Knowledge Base Management System for Supporting Advanced Applications. SIGMOD Conference 1993: 540-541
  7. Mingsen Guo, Stanley Y. W. Su, Herman Lam: An Association Algebra For Processing Object-Oriented Databases. ICDE 1991: 23-32
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