Xianmin Liu

On the complexity of sampling query feedback restricted database repair of functional dependency violations

An inconsistent database is a database instance violating integrity constraints. A repair of an inconsistent database is a maximal consistent subset. Sampling from the repair space is an alternative approach meeting the needs of many applications. In this paper, we introduce a new class of repair, query feedback restricted repair, based on the feedback on users witness query. We first map out a picture of both data and combined complexities of repair existence problems under different cases to identify the intractable cases. Especially, we show that if the query is a projection or a union query, then the decision problem is NP-complete; even worse, if the query is a conjunctive query, the decision problem becomes Σ 2 P -complete. However, we prove that the combined complexity of the repair existence problem is in LOGSPACE when the witness query is a selection-join query, and this conclusion also implies that the combined complexity of side-effect free deletion propagation problem under group-deletion is in LOGSPACE which is not considered in previous works. Additionally, we provide a polynomial random repair sampling algorithm under combined complexity. At last, we revisit the key preserving condition 1 and show that it will simplify the problem, i.e., some cases become tractable for certain key preserving views, as opposed to their counterparts that are not key preserving.

TKAP: Efficiently processing top-k query on massive data by adaptive pruning

In many applications, top-k query is an important operation to return a set of interesting points in a potentially huge data space. The existing algorithms, either maintaining too many candidates, or requiring assistant structures built on the specific attribute subset, or returning results with probabilistic guarantee, cannot process top-k query on massive data efficiently. This paper proposes a sorted-list-based TKAP algorithm, which utilizes some data structures of low space overhead, to efficiently compute top-k results on massive data. In round-robin retrieval on sorted lists, TKAP performs adaptive pruning operation and maintains the required candidates until the stop condition is satisfied. The adaptive pruning operation can be adjusted by the information obtained in round-robin retrieval to achieve a better pruning effect. The adaptive pruning rule is developed in this paper, along with its theoretical analysis. The extensive experimental results, conducted on synthetic and real-life data sets, show the significant advantage of TKAP over the existing algorithms.

Vertex Cover in Conflict Graphs: Complexity and a Near Optimal Approximation

Given finite number of forests of complete multipartite graph, conflict graph is a sum graph of them. Graph of this class can model many natural problems, such as in database application and others. We show that this property is non-trivial if limiting the number of forests of complete multipartite graph, then study the problem of vertex cover on conflict graph in this paper. The complexity results list as follow,If the number of forests of complete multipartite graph is fixed, conflict graph is non-trivial property, but finding 1.36-approximation algorithms is NP-hard.Given 2 forests of complete multipartite graph and maximum degree less than 7, vertex cover problem of conflict graph is NP-complete. Without the degree restriction, it is shown to be NP-hard to find an algorithm for vertex cover of conflict graph within

Tree size reduction with keeping distinguishability

\frac{17}{16}-\varepsilon

On the Complexity of Insertion Propagation with Functional Dependency Constraints

1716-e, for any

Discovery of Field Functional Dependencies

\varepsilon >0