Supporting Set Operations in Temporal-Probabilistic Databases

Abstract

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.

Outer and Anti Joins in Temporal-Probabilistic Databases

“…The union combining the subresults has to remove the unmatched windows that are computed twice and when used, the θ condition of the TP join is ignored. The optimizer opts for a nested loop for r❞⑤ ❃❁⑤ θo∧θ s and this takes a huge 1 The WebKit Open Source Project: http://www.webkit.org (2012) 2 Fig. 6: Negating Windows toll on TA's runtime making NJ two orders of magnitude faster.…”

“…III. ALGORITHMS In this section, we introduce two sweeping-window algorithms [1] for the computation of unmatched (LAWA U ) and negating (LAWA N ) windows. LAWA U is applied on the set of overlapping windows and LAWA N is applied on the windows produced by LAWA U .…”

Online Computing Quantile Summaries Over Uncertain Data Streams

“…There have been many works devoting to supporting uncertainty processing in database systems [30] or developing prototype systems for managing uncertain data, e.g., Trio [31], MystiQ [32], Orion [33], BayesStore [49] and Avatar [34]. Various uncertain data are considered in these works, including geo-spatial data [35], temporal-spatial data [28], [36], sensor data [11], [24], and data streams [1], [13], [14]. Besides, recent years have seen much works focusing on uncertain graph data in a variety of issues, e.g., uncertain graph modeling [37], processing [38], clustering [39], [40], querying [41], ranking [42], finding cliques [43], and decomposition [44].…”

A Hybrid Relational Database Model for Uncertain and Imprecise Information

“…Some models (e.g. [7], [8], [10], [12], [16], [19], [20], [22], [27], [28]) using only the probability theory could represent and handle uncertain information but not imprecise information of objects. Some other models (e.g.…”