Consider the schema BCDFGH with the following FDs: BG ? CD, G ? F , CD ? GH , C ? FG , F ? D. Use the 3NF synthesis algorithm to obtain a lossless, dependency preserving decomposition into 3NF. If any of the resulting schemas is not in BCNF, proceed to decompose them into BCNF.
What will be an ideal response?
Minimal cover: First, split the right-hand sides into BG ? C , BG ? D, CD ? G, CD ? H , C ? F ,andC ? G. Next reduce the left-hand sides. CD ? G reduces to C ? G (and is eliminated, since it is a duplicate), CD ? H reduces to C ? H ,and BG ? D reduces to G ? D. Thus, after the second step we end up with
BG ? C
G ? D
G ? F
C ? H
C ? F
C ? G
F ? D
The last stage eliminates the redundant FDs and we end up with:
BG ? C
G ? F
C ? H
C ? G
F ? D
A lossless, dependency-preserving decomposition into 3NF: (BGC ; {BG ? C , C ? G}), (GF ; {G ? F}), (CGH ; {C ? GH}), (FD; {F ? D}). The schema (BGC ; {BG ? C , C ? G}) is not in BCNF. A decomposition with respect to C ? G into (CG; {C ? G})and(CB; {}) brings it into BCNF, but looses the FD BG ? C .
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