Answering Why-Not questions consists in explaining to developers of complex data transformations or manipulations why their data transformation did not produce some specific results, although they expected them to do so. Different types of explanations that serve as Why-Not answers have been proposed in the past and are either based on the available data, the query tree, or both. Solutions (partially) based on the query tree are generally more efficient and easier to interpret by developers than solutions solely based on data. However, algorithms producing such query-based explanations so far may return different results for reordered conjunctive query trees, and even worse, these results may be incomplete. Clearly, this represents a significant usability problem, as the explanations developers get may be partial and developers have to worry about the query tree representation of their query, losing the advantage of using a declarative query language. As remedy to this problem, we propose the Ted algorithm that produces the same complete querybased explanations for reordered conjunctive query trees.

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Several application domains, including healthcare, smart building, and traffic monitoring, require the continuous publishing of data, also known as time series. In many cases, time series are geotagged data containing sensitive personal details, and thus their processing entails privacy concerns. Several definitions have been proposed that allow for privacy preservation while processing and publishing such data, with differential privacy being the most prominent one. Most existing differential privacy schemes protect either a single timestamp (event-level), or all the data per user (user-level), or per window (𝑤-event-level) in the time series, considering however all timestamps as equally significant. In this work, we define a novel configurable privacy notion, landmark privacy, which differentiates events into significant (landmarks) and regular, achieving to provide better data utility while preserving adequately the privacy of each event. We propose three schemes that guarantee landmark privacy, and design an appropriate dummy landmark selection module to better protect the actual temporal position of the landmarks. Finally, we provide a thorough experimental study where (i) we study the behavior of our framework on real and synthetic data, with and without temporal correlation, and (ii) demonstrate that landmark privacy achieves generally better data utility in the presence of landmarks than user-level privacy.