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Unformatted text preview: 202 Chapter 19 Exercise 19.28 Give an algorithm for testing whether a relation scheme is in BCNF. The algorithm should be polynomial in the size of the set of given FDs. (The size is the sum over all FDs of the number of attributes that appear in the FD.) Is there a polynomial algorithm for testing whether a relation scheme is in 3NF? Answer 19.28 Answer omitted. Exercise 19.29 Prove that the algorithm for decomposing a relation schema with a set of FDs into a collection of BCNF relation schemas as described in Section 19.6.1 is correct (i.e., it produces a collection of BCNF relations, and is lossless-join) and terminates. Answer 19.29 First, we will repeat the algorithm so as to keep consistent notation: 1. Let X R , A be a single atribute in R and X A be a FD that causes a violation of BCNF. Decompose into R A and XA . 2. If either R A or XA is not in BCNF, decompose them further by a recursive application of this algorithm. Proving the correctness of the algorithm is divided into 3 parts: Proof that every Decomposition is Lossless: For any decomposition of a relation R into R A and XA that the algorithm takes, it is trivially loseless by Thoerem 3 of this chapter. First, we claim thattakes, it is trivially loseless by Thoerem 3 of this chapter....
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This note was uploaded on 01/17/2012 for the course EGN 4302 taught by Professor Dr.vishak during the Fall '12 term at University of Central Florida.
- Fall '12