Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
An Algebraic Representation of Calendars
Annals of Mathematics and Artificial Intelligence
Symbolic User-Defined Periodicity in Temporal Relational Databases
IEEE Transactions on Knowledge and Data Engineering
Implementing Calendars and Temporal Rules in Next Generation Databases
Proceedings of the Tenth International Conference on Data Engineering
The SOL Time Theory: A Formalization of Structured Temporal Objects and Repetition
TIME '04 Proceedings of the 11th International Symposium on Temporal Representation and Reasoning
Recursive Representation of Periodicity and Temporal Reasoning
TIME '04 Proceedings of the 11th International Symposium on Temporal Representation and Reasoning
An Efficient Algorithm for Minimizing Time Granularity Periodical Representations
TIME '05 Proceedings of the 12th International Symposium on Temporal Representation and Reasoning
Representation of periodic moving objects in databases
GIS '06 Proceedings of the 14th annual ACM international symposium on Advances in geographic information systems
Evaluating Exceptions on Time Slices
ER '09 Proceedings of the 28th International Conference on Conceptual Modeling
Querying multi-granular compact representations
DASFAA'06 Proceedings of the 11th international conference on Database Systems for Advanced Applications
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Recurrences are defined as sets of time instants associated with events and they are present in many application domains, including public transport schedules and personal calendars. Because of their large size, recurrences are rarely stored explicitly, but some form of compact representation is used. Multislices are a compact representation that is well suited for storage in relational databases. A multislice is a set of time slices where each slice employs a hierarchy of time granularities to compactly represent multiple recurrences. In this paper we investigate the construction of multislices from recurrences. We define the compression ratio of a multislice, show that different construction strategies produce multislices with different compression ratios, and prove that the construction of minimal multislices, i.e., multislices with a maximal compression ratio, is an NP-hard problem. We propose a scalable algorithm, termed LMerge, for the construction of multislices from recurrences. Experiments with real-world recurrences from public transport schedules confirm the scalability and usefulness of LMerge: the generated multislices are very close to minimal multislices, achieving an average compression ratio of approx. 99%. A comparison with a baseline algorithm that iteratively merges pairs of mergeable slices shows significant improvements of LMerge over the baseline approach.