Operations on (ordered) interval sets

Intervals play an important role in various kinds of database-applications in practice, for example in historical, spatial, and temporal databases. As a consequence, there is a practical need for a clear and proper treatment of various useful operations on intervals and interval sets in a database context. However, the semantics of some important operations on interval sets are not always treated or not treated very clearly in the literature; e.g., often they are defined in an algorithmic rather than a declarative manner. Moreover, implementation proposals are often not as straightforward as they could be. This paper presents a declarative treatment of various operations on interval sets, also introducing some new notions (such as ordered interval sets, their visible points, and their surface). Then the paper formally ?links? such (mathematical) intervals to their database representations. Finally the paper provides straightforward translations from these formal database representations to standard SQL, without the need for SQL extensions.

Efficient Self-Join Algorithm in Interval-based Temporal Data Models

Interval-based temporal data model is a popular data model in temporal databases. It uses time intervals for representing the period of validity of a tuple, leading to unavoidable self-joins when combining tuples for objects. It requires k+1-way self-join for k conjunctive conditions. Join operations are one of the most expensive operations in databases and they are even more serious in temporal databases because of growing data. There are many join algorithms for temporal databases. However, they focus on joining different inputs rather than an identical input, leading to multiple scans for the identical input. Advanced 2-way join algorithms avoid a quadratic disk I/O complexity, but they are affected by the number of self-joins and partition sizes. In this paper, we address the problem of self-joins in the interval-based temporal data model and introduce a stream-based self-join algorithm. The proposed algorithm shows that it achieves a single relation scan for k-way self-join and its performance is not affected by partition sizes

An XML-based implementation of the parametric model for ad-hoc query of temporal and spatiotemporal data

The parametric model is one of the data models for dimensional data. Values in the parametric model are defined as functions. Such modeling concept helps one achieve a one-to-one correspondence between objects in the real world and records in a database. One of the important requirements is that domains of values should be closed under the set theoretic operations such as union, intersection, and complementation. Because of this, ParaSQL, a query language of the parametric model, is able to mimic natural languages more closely. In this dissertation we validate and implement the parametric model for temporal and spatiotemporal data. We also develop a preliminary prototype for the users of NC-94, an interesting dataset in agriculture;Viewing values as functions leads variable-length tuples. Potentially, such values vary in size ranging from a few bytes to gigabytes and beyond. This makes implementation of the parametric model a challenging problem. To meet the challenge, we develop an XML-based storage and deploy it in our implementation. Incidentally, XML is also used for interfacing various modules and artifacts like parse tree, expression tree, and iterators to fetch data from a disk;The NC-94 dataset, mentioned above, contains the most complete record of spatiotemporal variables that characterize the dynamics of agriculture covering the north central region in the United States. To support ad-hoc query of data in its geospatial context, a novel hybrid structure is designed and implemented. We use GML to describe geospatial information. Use of GML is a good match, because it is XML-based. More importantly, it meets the set theoretic closure requirements proposed by the parametric model;Validation and implementation methodologies introduced in this dissertation will contribute to database and GIS communities. The validation demonstrates the ease of use and efficiency of the parametric model for temporal and spatiotemporal data. This should help settle a debate in temporal database community which has continued since the mid 1980s. The findings also extend to spatial and spatiotemporal data. It is an important baby-step toward full-fledged implementation of the parametric model. We hope that this work will also help bring database and GIS communities together

Formal extension of the relational model for the management of spatial and spatio-temporal data

[Resumen] En los últioms años, se ha realizado un gran esfuerzo investigador en la manipulación de datos especiales y Sistemas de Información Geográfica (SIG). Una clara limitación de las primeras aproximaciones es la falta de integración entre datos geográficos y alfanuméricos. Para resolver esto surge el área de Bases de Datos Espaciales. Los problemas que aparecen en este campo son muchos y complejos. Un primer ejemplo son las peculiaridades de las operaciones espaciales, como el calculo de la intersección espacial de dos superficies. Otro ejemplo es el elegir las estructuras de datos apropiadas (relaciones, capas, etc.) y el conjunto de operaciones adeucado. La combinación con las Bases de Datos Temporales da lugar a las Bases de Datos Espacio-temporales, en las que la inclusión de la dimensión temporal complica más los problemas anteriores. A pesar de la gran cantidad de aproximaciones propuestas, no se ha llegado todavía a una solución satisfactoria. La presente tesis propone una nueva solución que resuelve todos los problemas de modelado de datos espaciales y espacio-temporales resaltados arriba. Parte del trabajo se completó durante el proyecto ""CHOROCRONOS"": A Research Network for Saptiotemporal Database Systems"", financiado por la Unión Europea. El modelo propuesto en la tesis define tres tipos de dato punto, línea y superficie, que encajan perfectamente en la percepción humana. La definición de estos tipos de dato se basa en la definición previa de Quanta Espacial. Las estructuras de datos usadas son las relaciones no anidadas de modelo relacional puro. El conjunto de operaciones relacionales permite alcanzar casi por completo la funcionalidad propuesta en otros modelos. Todas las operaciones han sido definidas en base a un núcleo reducido de operaciones primitvas. Todos los tipos de datos, espaciales, espacio-temporales y convencionales se manipulan de forma uniforme con este conjunto de operaciones