On the representation and querying of sets of possible worlds
SIGMOD '87 Proceedings of the 1987 ACM SIGMOD international conference on Management of data
The anatomy of a large-scale hypertextual Web search engine
WWW7 Proceedings of the seventh international conference on World Wide Web 7
Two Algorithms for Determining Volumes of Convex Polyhedra
Journal of the ACM (JACM)
The Management of Probabilistic Data
IEEE Transactions on Knowledge and Data Engineering
Learning Probabilistic Relational Models
IJCAI '99 Proceedings of the Sixteenth International Joint Conference on Artificial Intelligence
Optimal aggregation algorithms for middleware
Journal of Computer and System Sciences - Special issu on PODS 2001
Optimizing Top-k Selection Queries over Multimedia Repositories
IEEE Transactions on Knowledge and Data Engineering
Ranking objects based on relationships
Proceedings of the 2006 ACM SIGMOD international conference on Management of data
Proceedings of the 2006 ACM SIGMOD international conference on Management of data
Management of probabilistic data: foundations and challenges
Proceedings of the twenty-sixth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Ranking queries on uncertain data: a probabilistic threshold approach
Proceedings of the 2008 ACM SIGMOD international conference on Management of data
Efficient Processing of Top-k Queries in Uncertain Databases with x-Relations
IEEE Transactions on Knowledge and Data Engineering
Semantics of Ranking Queries for Probabilistic Data and Expected Ranks
ICDE '09 Proceedings of the 2009 IEEE International Conference on Data Engineering
ICDE '09 Proceedings of the 2009 IEEE International Conference on Data Engineering
A unified approach to ranking in probabilistic databases
Proceedings of the VLDB Endowment
Ranking continuous probabilistic datasets
Proceedings of the VLDB Endowment
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The goal of top-k ranking for objects is to rank the objects so that the best k of them can be determined. In this paper we consider an object to be an entity which consists of a number of attributes whose roles in the object are determined by an aggregation function. The problem of top-ranking in this case is conceptually simple for data that are complete and certain - the aggregation value of an object represents its strength and therefore its rank. For uncertain data, the semantic basis of top-k objects becomes unclear. In this paper, we formulate a semantics of top-k ranking for objects modeled by uncertain data, where the values of an object's attributes are expressed by probability distributions and constrained by some stated conditions. Under this setting, we present a theory of top-k ranking for objects so that their strengths can be determined in the presence of uncertain data. We present our theory in three stages. The first deals with discrete domains, which is extended to include continuous domains. We show that top-k ranking for objects in this context is closely related to high-dimensional space studied in mathematics. In particular, the computation of the volumes of a high-dimensional polyhedron represented by a system of linear inequations is a special case of top-k ranking under our theory. We further extend this theory to add weights to objects' positions and aggregation values in determining ranking results. We show that a number of previous proposals for top-k ranking are special cases of our theory.