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Chase (Algorithm)

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The chase algorithm is an algorithm in database construction, to test if a decomposition is lossless

Snippet from Wikipedia: Chase (algorithm): The chase is a simple fixed-point algorithm testing and enforcing implication of data dependencies in database systems. It plays important roles in database theory as well as in practice. It is used, directly or indirectly, on an everyday basis by people who design databases, and it is used in commercial systems to reason about the consistency and correctness of a data design. New applications of the chase in meta-data management and data exchange are still being discovered.
The chase has its origins in two seminal papers of 1979, one by Alfred V. Aho, Catriel Beeri, and Jeffrey D. Ullman and the other by David Maier, Alberto O. Mendelzon, and Yehoshua Sagiv.
In its simplest application the chase is used for testing whether the projection of a relation schema constrained by some functional dependencies onto a given decomposition can be recovered by rejoining the projections. Let t be a tuple in $\pi _{S_{1}}(R)\bowtie \pi _{S_{2}}(R)\bowtie ...\bowtie \pi _{S_{k}}(R)$ where R is a relation and F is a set of functional dependencies (FD). If tuples in R are represented as t₁, ..., t_k, the join of the projections of each t_i should agree with t on $\pi _{S_{i}}(R)$ where i = 1, 2, ..., k. If t_i is not on $\pi _{S_{i}}(R)$ , the value is unknown.
The chase can be done by drawing a tableau (which is the same formalism used in tableau query). Suppose R has attributes A, B, ... and components of t are a, b, .... For t_i use the same letter as t in the components that are in S_i but subscript the letter with i if the component is not in S_i. Then, t_i will agree with t if it is in S_i and will have a unique value otherwise.
The chase process is confluent. There exist implementations of the chase algorithm, some of them are also open-source.

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