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Anatomy of the Chase

Grahne G., Onet A.

Fundamenta Informaticae

2018

Vol. 157, nr 3

221--270

A lot of research activity has recently taken place around the chase procedure, due to its usefulness in data integration, data exchange, query optimization, peer data exchange and data correspondence, to mention a few. As the chase has been investigated and further developed by a number of research groups and authors, many variants of the chase have emerged and associated results obtained. Due to the heterogeneous nature of the area it is frequently difficult to verify the scope of each result. In this paper we take closer look at recent developments, and provide additional results. Our analysis allows us create a taxonomy of the chase variations and the properties they satisfy. Two of the most central problems regarding the chase is termination, and discovery of restricted classes of sets of dependencies that guarantee termination of the chase. The search for the restricted classes has been motivated by a fairly recent result that shows that it is undecidable (RE-complete, to be more precise) to determine whether the chase with a given dependency set will terminate on a given instance. There is a small dissonance here, since the quest has been for classes of sets of dependencies guaranteeing termination of the chase on all instances, even though the latter problem was not known to be undecidable. We resolve the dissonance in this paper by showing that determining whether the chase with a given set of dependencies terminates on all instances is unsolvable, and on level Π02 in the Arithmetical Hierarchy. For this we use a reduction from word rewriting systems, thereby also showing the close connection between the chase and word rewriting. The same reduction also gives us the aforementioned instancedependent RE-completeness result as a byproduct. For one of the restricted classes guaranteeing termination on all instances, the stratified sets dependencies, we provide new complexity results for the problem of testing whether a given set of dependencies belongs to it. These results rectify some previous claims that have occurred in the literature.

Privacy Aware Data Management and Chase

Im S.

Fundamenta Informaticae

2007

Vol. 78, nr 4

507-524

One of the key applications that uses the knowledge discovered by data mining is called Chase. Chase is a process that replaces null or missing values with the values predicted by the knowledge, and it is mainly used to obtain more complete information systems or to replace unknown attribute values in user queries. The process improves the quality of query answers with increased volume of reliable data, and helps the system understand user queries that would otherwise be difficult. However, a security breach may occur when a set of data in an information system is confidential. The confidential data can be hidden from the public view. However, Chase has the capability to reveal the hidden data by classifying them as null or missing. In this paper, we discuss disclosure of confidential data by Chase and protection algorithms that reduce the risk. In particular, the proposed algorithms aim to protect confidential data with the least amount of additional data hiding.