Lineage-Aware Temporal Windows: Supporting Set Operations in Temporal-Probabilistic Databases

TL;DR

This paper introduces lineage-aware temporal windows and the LAWA algorithm to efficiently perform set operations in temporal-probabilistic databases, reducing computational complexity from quadratic to linearithmic.

Contribution

It formally defines set operation semantics in TP databases and proposes a novel lineage-aware window mechanism with an efficient advancer for linearithmic computation.

Findings

Outperforms existing methods in synthetic and real datasets.

Performance depends only on input size, not interval overlap.

Guarantees no extra computational cost or buffer space.

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.