Efficient Updates of Uncertain Databases

Uncertain databases have evolved as an active area of database research, surveyed, for example, in [10].The possible worlds semantics [1] is commonly used to deal with uncertain data. Several representation systems for uncertain databases have been proposed to provide efficient storage and query facilities for a potentially big number of possible worlds, see, e.g., [14,4,8]. Antova et al. introduced U-relations [2], which guarantee polynomial data complexity for queries of positive relational algebra (RA, for short). U-relations have been implemented and are available in the MayBMS system [6]. As in the case of certain databases, we clearly also want to update uncertain databases and pose queries of unrestricted RA. In [3], an API for uncertain databases, which also covers updates, is presented. The paper mentions that, for updates, decompression of the succinct representation of the possible worlds may be necessary. However, it leaves open the details and also the question if decompression could at least partly be avoided by some extension of the representation system. While the evaluation of positive RA queries on uncertain databases has been studied extensively, there has been little work beyond positive RA, like queries with having clauses [7] and queries with one level of anti-join (not-exists [13]). Fink et al. [5] describe an approach for unrestricted RA queries, but in a formalism that does not exhibit polynomial time data complexity for computing possible answers. The goal of this work is to start the investigation of the update problem of U-relations and to tackle the problem of evaluating queries with anti-joins over this formalism. To this end, we will first define the anti-join operator for U-relations and show how to use it to model updates. It will turn out that the decompression of the succinct representation of possible worlds may indeed be a performance problem. We will therefore introduce an extension of the Urelation representation system and show that our new formalism may lead to an exponential decrease in the representation of an updated uncertain database. Our main contributions will be as follows.