@techreport{ilprints703,
          number = {2005-39},
          author = {Omar Benjelloun and Anish Das Sarma and Alon Halevy and Jennifer Widom},
            note = {A previous version of the paper was titled: "The Symbiosis of Lineage and Uncertainty"},
           title = {ULDBs: Databases with Uncertainty and Lineage},
            type = {Technical Report},
       publisher = {Stanford},
            year = {2005},
     institution = {Stanford InfoLab},
         journal = {Technical Report},
        keywords = {Data uncertainty, lineage (provenance); data modeling; probabilistic databases;},
             url = {http://ilpubs.stanford.edu:8090/703/},
        abstract = {This paper introduces \uldb s, an extension of relational databases with simple yet expressive constructs for representing and manipulating both {\em lineage} and {\em uncertainty}. Uncertain data and data lineage are two important areas of data management that have been considered extensively but in isolation, however many applications require the features in tandem. Fundamentally, lineage enables simple and consistent representation of uncertain data, it correlates uncertainty in query results with uncertainty in the input data, and query processing with lineage and uncertainty together presents computational benefits over treating them separately. We show that the \uldb\ representation is {\em complete}, and that it permits straightforward implementation of many relational operations. We define two notions of \uldb\ minimality---{\em data-minimal} and {\em lineage-minimal}---and study minimization of \uldb\ representations under both notions. With lineage, derived relations are no longer self-contained: their uncertainty depends on uncertainty in the base data. We provide algorithms for the new operation of extracting a database subset in the presence of interconnected uncertainty. Finally, we show how \uldbs enable a new approach to query processing in probabilistic databases. \uldb s form the basis of the {\em Trio} system, under development at Stanford.}
}