CONCLUSION
This dissertation studies the key problem of computational complexity and algorithm for data eval- uation and repairing. This dissertation first studies the computational complexity of and algorithms for the database inconsistency evaluation. We define and use the minimum tuple deletion to evaluate the database inconsistency. For such minimum tuple deletion problem, we study the relationship between the size of rule set and its computational complexity. We show that the minimum tuple deletion problem is still NP-complete, if given two conditional functional dependencies and three attributes involved in them;
And it is NP-hard to approximate the minimum tuple deletion problem within 1716 if given three conditional
functional dependencies and four attributes involved in them. We design a near optimal approximated
algorithm for computing the minimum tuple deletion, the ratio is 2− 1
2r, wherer is the number of condi-
tional functional dependencies in the given rule set Σ. Under the unique gaming conjecture, this ratio is
near optimal, its hard to improve it with a constant independent ofn.
To guide the data repairing, this dissertation also investigates the data repairing method by using query feedbacks, formally studies two decision problems, functional dependency restricted deletion and insertion propagation problem, corresponding to the feedbacks of deletion and insertion. A comprehensive analysis on both combined and data complexity of the cases is provided by considering different rela- tional operators and feedback types. We have identified the intractable and tractable cases to picture the complexity hierarchy of these problems, and provided the efficient algorithm on these tractable cases.
We also examine the complexity of the resilience decision problem by means of parameterized com- plexity. We find that a triangle query is fixed parameter tractable if the data is of planarity property with
the triangle query. Our result implies that if the solution of RES is bounded by k, then the data could be
pre-processed (kernelized) as a much simpler graph which has only O(k2) facts.
From the results, we know that when data volume becomes big, automatic propagation analysis is solvable in polynomial time. Unfortunately, when a conjunctive query becomes complex simultaneously, it is intractable even for the bounded case. Our work also makes contributions to the previous results for the problems of side-effect free deletion propagation, and could be applied in the update forbidden case of view propagation.
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