Computational Complexity And Algorithms For Dirty Data Evaluation And Repairing

In this dissertation, we study the dirty data evaluation and repairing problem in relational database. Dirty data is usually inconsistent, inaccurate, incomplete and stale. Existing methods and theories of consistency describe using integrity constraints, such as data dependencies. However, integrity constraints are good at detection but not at evaluating the degree of data inconsistency and cannot guide the data 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 NP-hard to approximate the minimum tuple deletion within 17/16 if given three functional dependencies and four attributes involved. A near optimal approximated algorithm for computing the minimum tuple deletion is proposed with a ratio of 2 − 1/2r , where r is the number of given functional dependencies. 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 relational 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. Two improvements are proposed, one focuses on figuring out the minimum vertex cover in conflict graph to improve the upper bound of tuple deletion problem, and the other one is a better dichotomy for deletion and insertion propagation problems at the absence of functional dependencies from the point of respectively considering data, combined and parameterized complexities

Finding a Collective Set of Items: From Proportional Multirepresentation to Group Recommendation

We consider the following problem: There is a set of items (e.g., movies) and a group of agents (e.g., passengers on a plane); each agent has some intrinsic utility for each of the items. Our goal is to pick a set of $K$ items that maximize the total derived utility of all the agents (i.e., in our example we are to pick $K$ movies that we put on the plane's entertainment system). However, the actual utility that an agent derives from a given item is only a fraction of its intrinsic one, and this fraction depends on how the agent ranks the item among the chosen, available, ones. We provide a formal specification of the model and provide concrete examples and settings where it is applicable. We show that the problem is hard in general, but we show a number of tractability results for its natural special cases