  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.
