Constant-time maintainability: a generalization of independence

  • Authors:

  • Ke Wang;Marc H. Graham

  • Affiliations:

  • Chongqing Univ., Chongqing, China;Carnegie Mellon Univ., Pittsburgh, PA

  • Venue:
  • ACM Transactions on Database Systems (TODS)
  • Year:
  • 1992

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Abstract

The maintenance problem of a database scheme is the following decision problem: Given a consistent database state &rgr; and a new tuple u over some relation scheme of &rgr;, is the modified state &rgr; ∪ {u} still consistent? A database scheme is said to be constant-time-maintainable(ctm) if there exists an algorithm that solves its maintenance problem by making a fixed number of tuple retrievals. We present a practically useful algorithm, called the canonical maintenance algorithm, that solves the maintenance problem of all ctm database schemes within a "not too large" bound. A number of interesting properties are shown for ctm database schemes, among them that non-ctm database schemes are not maintainable in less than a linear time in the state size. A test method is given when only cover embedded functional dependencies (fds) appear. When the given dependencies consist of fds and the join dependency (jd) ⋈ R of the database scheme, testing whether a database scheme is ctm is reduced to the case of cover embedded fds. When dependency-preserving database schemes with only equality-generating dependencies (egds) are considered, it is shown that every ctm database scheme has a set of dependencies that is equivalent to a set of embedded fds, and thus, our test method for the case of embedded fds can be applied. In particular, this includes the important case of lossless database schemes with only egds.