12,443 research outputs found
Scalable Probabilistic Similarity Ranking in Uncertain Databases (Technical Report)
This paper introduces a scalable approach for probabilistic top-k similarity
ranking on uncertain vector data. Each uncertain object is represented by a set
of vector instances that are assumed to be mutually-exclusive. The objective is
to rank the uncertain data according to their distance to a reference object.
We propose a framework that incrementally computes for each object instance and
ranking position, the probability of the object falling at that ranking
position. The resulting rank probability distribution can serve as input for
several state-of-the-art probabilistic ranking models. Existing approaches
compute this probability distribution by applying a dynamic programming
approach of quadratic complexity. In this paper we theoretically as well as
experimentally show that our framework reduces this to a linear-time complexity
while having the same memory requirements, facilitated by incremental accessing
of the uncertain vector instances in increasing order of their distance to the
reference object. Furthermore, we show how the output of our method can be used
to apply probabilistic top-k ranking for the objects, according to different
state-of-the-art definitions. We conduct an experimental evaluation on
synthetic and real data, which demonstrates the efficiency of our approach
Fast and Simple Relational Processing of Uncertain Data
This paper introduces U-relations, a succinct and purely relational
representation system for uncertain databases. U-relations support
attribute-level uncertainty using vertical partitioning. If we consider
positive relational algebra extended by an operation for computing possible
answers, a query on the logical level can be translated into, and evaluated as,
a single relational algebra query on the U-relation representation. The
translation scheme essentially preserves the size of the query in terms of
number of operations and, in particular, number of joins. Standard techniques
employed in off-the-shelf relational database management systems are effective
for optimizing and processing queries on U-relations. In our experiments we
show that query evaluation on U-relations scales to large amounts of data with
high degrees of uncertainty.Comment: 12 pages, 14 figure
Query Evaluation in Deductive Databases
It is desirable to answer queries posed to deductive databases by computing fixpoints because such computations are directly amenable to set-oriented fact processing. However, the classical fixpoint procedures based on bottom-up processing — the naive and semi-naive methods — are rather primitive and often inefficient. In this article, we rely on bottom-up meta-interpretation for formalizing a new fixpoint procedure that performs a different kind of reasoning: We specify a top-down query answering method, which we call the Backward Fixpoint Procedure. Then, we reconsider query evaluation methods for recursive databases. First, we show that the methods based on rewriting on the one hand, and the methods based on resolution on the other hand, implement the Backward Fixpoint Procedure. Second, we interpret the rewritings of the Alexander and Magic Set methods as specializations of the Backward Fixpoint Procedure. Finally, we argue that such a rewriting is also needed in a database context for implementing efficiently the resolution-based methods. Thus, the methods based on rewriting and the methods based on resolution implement the same top-down evaluation of the original database rules by means of auxiliary rules processed bottom-up
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