In temporal-probabilistic (TP) databases, the combination of the temporal and the probabilistic dimension adds significant overhead to the computation of set operations. Although set queries are guaranteed to yield linearly sized output relations, existing solutions exhibit quadratic runtime complexity. They suffer from redundant interval comparisons and additional joins for the formation of lineage expressions. In this paper, we formally define the semantics of set operations in TP databases and study their properties. For their efficient computation, we introduce the lineage-aware temporal window, a mechanism that directly binds intervals with lineage expressions. We suggest the lineage-aware window advancer (LAWA) for producing the windows of two TP relations in linearithmic time, and we implement all TP set operations based on LAWA. By exploiting the flexibility of lineage-aware temporal windows, we perform direct filtering of irrelevant intervals and finalization of output lineage expressions and thus guarantee that no additional computational cost or buffer space is needed. A series of experiments over both synthetic and real-world datasets show that (a) our approach has predictable performance, depending only on the input size and not on the number of time intervals per fact or their overlap, and that (b) it outperforms state-of-the-art approaches in both temporal and probabilistic databases.

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The result of a temporal-probabilistic (TP) join with negation includes, at each time point, the probability with which a tuple of a positive relation p matches none of the tuples in a negative relation n, for a given join condition . For the computation of TP joins with negation, we introduce generalized lineage-aware temporal windows, a mechanism that binds an interval to the lineages of all the matching valid tuples of each input relation. We compute these windows in an incremental manner, and we show that pipelined computations allow for the direct integration of our approach into PostgreSQL. We thereby alleviate the prevalent redundancies in the interval computations of existing approaches, which is proven by an extensive experimental evaluation with real-world datasets.Abstract-The result of a temporal-probabilistic (TP) join with negation includes, at each time point, the probability with which a tuple of a positive relation p matches none of the tuples in a negative relation n, for a given join condition θ. For the computation of TP joins with negation, we introduce generalized lineage-aware temporal windows, a mechanism that binds an interval to the lineages of all the matching valid tuples of each input relation. We compute these windows in an incremental manner, and we show that pipelined computations allow for the direct integration of our approach into PostgreSQL. We thereby alleviate the prevalent redundancies in the interval computations of existing approaches, which is proven by an extensive experimental evaluation with real-world datasets.

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