Subject: Databases

Question: Consider the universal relation R = {A, B, C, D, E, F, G, H, I, J} and the set of functional dependencies G = { {A, B} -> {C}, {B, D} -> {E, F}, {A, D} -> {G, H}, {A} -> {I}, {H} -> {J} }. What is the key for R? Decompose R into 2NF, then 3NF relations. Hint: use Algorithm 15.4.

Algorithm 15.4 Relational Synthesis into 3NF with Dependency Preservation and Non-Additive (Lossless) Join Property Input: A universal relation R and a set of functional dependencies F on the attributes of R. 1. Find a minimal cover G for F (use Algorithm 15.0). 2. For each left-hand-side X of a functional dependency that appears in G, create a relation schema in D with attributes Xu (A1 (A2 u where X A1, X-> A2, , x->Ak are the only dependencies in G with X as left-hand-side (X is the key of this relation). 3. If none of the relation schemas in D contains a key of R, then create one more relation schema in D that contains attributes that form a key of R. (Use Algorithm 15.4a to find the key of R)