Dimensional Inconsistency Measures and Postulates in Spatio-Temporal Databases

The problem of managing spatio-temporal data arises in many applications, such as location-based services, environmental monitoring, geographic information systems, and many others. Often spatio-temporal data arising from such applications turn out to be inconsistent, i.e., representing an impossible situation in the real world. Though several inconsistency measures have been proposed to quantify in a principled way inconsistency in propositional knowledge bases, little effort has been done so far on inconsistency measures tailored for the spatio-temporal setting. In this paper, we define and investigate new measures that are particularly suitable for dealing with inconsistent spatio-temporal information, because they explicitly take into account the spatial and temporal dimensions, as well as the dimension concerning the identifiers of the monitored objects. Specifically, we first define natural measures that look at individual dimensions (time, space, and objects), and then propose measures based on the notion of a repair. We then analyze their behavior w.r.t. common postulates defined for classical propositional knowledge bases, and find that the latter are not suitable for spatio-temporal databases, in that the proposed inconsistency measures do not often satisfy them. In light of this, we argue that also postulates should explicitly take into account the spatial, temporal, and object dimensions and thus define “dimension-aware” counterparts of common postulates, which are indeed often satisfied by the new inconsistency measures. Finally, we study the complexity of the proposed inconsistency measures.

Efficient Discovery of Periodic-Frequent Patterns in Columnar Temporal Databases

Discovering periodic-frequent patterns in temporal databases is a challenging problem of great importance in many real-world applications. Though several algorithms were described in the literature to tackle the problem of periodic-frequent pattern mining, most of these algorithms use the traditional horizontal (or row) database layout, that is, either they need to scan the database several times or do not allow asynchronous computation of periodic-frequent patterns. As a result, this kind of database layout makes the algorithms for discovering periodic-frequent patterns both time and memory inefficient. One cannot ignore the importance of mining the data stored in a vertical (or columnar) database layout. It is because real-world big data is widely stored in columnar database layout. With this motivation, this paper proposes an efficient algorithm, Periodic Frequent-Equivalence CLass Transformation (PF-ECLAT), to find periodic-frequent patterns in a columnar temporal database. Experimental results on sparse and dense real-world and synthetic databases demonstrate that PF-ECLAT is memory and runtime efficient and highly scalable. Finally, we demonstrate the usefulness of PF-ECLAT with two case studies. In the first case study, we have employed our algorithm to identify the geographical areas in which people were periodically exposed to harmful levels of air pollution in Japan. In the second case study, we have utilized our algorithm to discover the set of road segments in which congestion was regularly observed in a transportation network.

Cache-efficient sweeping-based interval joins for extended Allen relation predicates

We develop a family of efficient plane-sweeping interval join algorithms for evaluating a wide range of interval predicates such as Allen’s relationships and parameterized relationships. Our technique is based on a framework, components of which can be flexibly combined in different manners to support the required interval relation. In temporal databases, our algorithms can exploit a well-known and flexible access method, the Timeline Index, thus expanding the set of operations it supports even further. Additionally, employing a compact data structure, the gapless hash map, we utilize the CPU cache efficiently. In an experimental evaluation, we show that our approach is several times faster and scales better than state-of-the-art techniques, while being much better suited for real-time event processing.

Checking Sets of Pure Evolving Association Rules

Extracting association rules from large datasets has been widely studied in many variants in the last two decades; they allow to extract relations between values that occur more “often” in a database. With temporal association rules the concept has been declined to temporal databases. In this context the “most frequent” patterns of evolution of one or more attribute values are extracted. In the temporal setting, especially where the interference betweeen temporal patterns cannot be neglected (e.g., in medical domains), there may be the case that we are looking for a set of temporal association rules for which a “significant” portion of the original database represents a consistent model for all of them. In this work, we introduce a simple and intuitive form for temporal association rules, called pure evolving association rules (PE-ARs for short), and we study the complexity of checking a set of PE-ARs over an instance of a temporal relation under approximation (i.e., a percentage of tuples that may be deleted from the original relation). As a by-product of our study we address the complexity class for a general problem on Directed Acyclic Graphs which is theoretically interesting per se.