# Accession Number:

## ADA135105

# Title:

## On Acyclic Database Decompositions.

# Descriptive Note:

## Technical rept.,

# Corporate Author:

## STANFORD UNIV CA DEPT OF COMPUTER SCIENCE

# Report Date:

## 1983-07-01

# Pagination or Media Count:

## 13.0

# Abstract:

Given a universal relation scheme, presented as a set of attributes and a set of dependencies, it may be advantageous ot decompose it into a collection of schemes, each with its own sets of attributes and dependencies, which has some desired properties. A basic requirement for such a decomposition to be useful is that the corresponding decomposition map on universal relations be injective. A central problem in database theory is to find the reconstruction map, i.e., the inverse map of an injective decomposition map. We prove here that when the decomposition, viewed as a hypergraph, is acrylic and the given dependencies are full implicational dependencies, then the reconstruction map is the natural join. Based on this, we show that there is a polynomial time algorithm to test for injectiveness of decompositions.

# Descriptors:

# Subject Categories:

- Theoretical Mathematics