Ordered Types in the AQUA Data Model

We present a query algebra that supports ordering among the data elements. Order is defined as a relationship between various data elements of an instance. This relationship can be a total or partial order among the elements or among equivalence classes where each equivalence class consists of one or more elements. In terms of data structures, ordered types can be viewed as graphs, trees, or lists. Lately there has been a lot of interest in bulk types like lists, trees, and graphs that are not supported by traditional data models and query algebras. This interest is fueled by the fact that much of the data in the scientific domain is inherently ordered. Therefore, scientific applications that involve genome sequences, satellite data, scientific data, etc. require database support for ordered data structures like lists, trees, and graphs. In this paper, we discuss the AQUA query algebra and its associated data model with special emphasis on ordered types and their operators.