Peter J. H. King

Querying multi-dimensional data indexed using the Hilbert space-filling curve

Mapping to one-dimensional values and then using a one-dimensional indexing method has been proposed as a way of indexing multi-dimensional data. Most previous related work uses the Z-Order Curve but more recently the Hilbert Curve has been considered since it has superior clustering properties. Any approach, however, can only be of practical value if there are effective methods for executing range and partial match queries. This paper describes such a method for the Hilbert Curve.

Using Space-Filling Curves for Multi-dimensional Indexing

This paper presents and discusses a radically different approach to multi-dimensional indexing based on the concept of the space-filling curve. It reports the novel algorithms which had to be developed to create the first actual implementation of a system based on this approach, on some comparative performance tests, and on its actual use within the TriStarp Group at Birkbeck to provide a Triple Store repository. An important result that goes beyond this requirement, however, is that the performance improvement over the Grid File is greater the higher the dimension.

Using state diagrams for Hilbert curve mappings

The Hilbert Curve describes a method of mapping between one and n dimensions. Such mappings are of interest in a number of application domains including image processing and, more recently, in the indexing of multi-dimensional data. Relatively little work, however, has been devoted to techniques for mapping in more that 2 dimensions. This paper presents a technique for constructing state diagrams to facilitate mappings and is a specialization of an incomplete generic process described by Bially. Although the storage requirements for state diagrams increase exponentially with the number of dimensions, they are useful in up to about 9 dimensions.

Syntax and Semantics of Gql, a Graphical Query Language

Abstract The problem of formalization for visual languages has been identified as an important one. We present in this paper a formal definition of both the syntax and semantics of Gql, a declarative graphical query language based on the functional data model. In Gql a query is fully and unambiguously represented by a single diagram and the user interaction is kept distinct from the language itself. In our approach for formalization we abstract from the world of graphics and concentrate on a world of sets and functions, called the base structure, which represent the various elements of the language. The syntactical definition of the language is completed by defining a set of rules that a base structure instance must satisfy, in order for it to correspond to a legal Gql query. The semantics of the language is given via a functionally defined, syntax-directed translation from Gql queries (represented as base structure instances) to list comprehensions. Finally, a form of attribute grammar is used in conjunction with the previous definitions for specifying in a single formalism both the syntax and semantics of Gql.

Extending the functional data model to computational completeness

We introduce the functional database language FDL which extends the functional data model to computational completeness while also supporting the persistence of any function, whether extensionally or intentionally defined. FDL improves on previous implementations of the functional data model by providing a uniform formalism both for modelling data and for computation, by supporting arbitrarily nested data types which are all persistent, and by allowing for the representation of incomplete and default knowledge. All functions are updated incrementally by the insertion and deletion of individual equations and an integrity sub-system verifies updates against the declared semantic integrity constraints.

Gql, a declarative graphical query language based on the functional data model

We present in this paper Gql, a declarative graphical query language based on the functional data model. Gql queries are fully represented by a single diagram. Without containing any explicit boolean operators or logical quantifiers, Gql provides users of varying degrees of programming experience, with the same expressive power for retrieval as SQL. The design philosophy and characteristics of the language are discussed, and an informal presentation of Gqls constructs and semantics is given. Finally, gql_int, the implementation of an interface for the language, is described.

The Functional Approach to Data Management

point x-coord point -) num y-cood .. point -) num weight .. point -) num Suppose a particular application is much concerned with the distance between pairs of points. It would then clearly be useful to have a function to provide this directly as part of the user view. This can be achieved by including in the view specification the function definition dist point dist p1 p2 = point -> num; let x = (x-coord p1) let y = (y-coord p1) in sqrt (x*x+y*y);

A Graph-Rewriting Visual Language for Database Programming

Abstract Textual database programming languages are computationally complete, but have the disadvantage of giving the user a non-intuitive view of the database information that is being manipulated. The visual languages developed in recent years have allowed naive users access to a direct representation of data, often in a graph form, but have concentrated on user interface rather than complex programming tasks. There is a need for a system which combines the advantages of both these programming methods. We describe an implementation of Spider, an experimental visual database programming language aimed at programmers. It uses a graph-rewriting paradigm as a basis for a fully visual, computationally complete language. The graphs it rewrites represent the schema and instances of a database. The unique graph-rewriting method used by Spider has syntactic and semantic simplicity. Its form of algorithmic expression allows complex computation to be easily represented in short programs. Furthermore, Spider has greater power than normally provided in textual systems, and we show that queries on the schema and associative queries can be performed easily and without requiring any additions to the language.

Querying Graph Databases Using a Functional Language Extended with Second Order Facilities

This paper presents the functional database language Hydra which extends previous such languages with associational facilities enabling a user to pose queries about the ways in which values and entities in the database are related to each other. These associational facilities work by treating the database as a graph and following all the arcs from a node or finding paths between nodes. The nodes of the database graph correspond to entities or values in the application domain and the arcs to associations between those entities and values. From the perspective of Hydra this database graph is viewed in terms of functions between sets of entities and values. Associational facilities are provided by built-in second-order primitives which use schema-level information to determine what arcs may be associated with a node or as the basis for searching for an instance-level path. Results from associational primitives are returned in the form of lists of functions which may be displayed to the user or directly applied to other parameters. The associational facilities provided are fully integrated into a computationally complete language in the style of Miranda. This integration allows complex queries to be answered, which are beyond the power of conventional database query languages.

Incrementally visualising criminal networks

Understanding the information gathered thus far in a criminal investigation is of great importance, particularly in terms of guiding its future course. Since the late 1980s the use of software tools to provide visualisations of this information has become increasingly common. The objective of such tools is to provide, in a readily comprehensible way, the social network of all the people involved. This may include the victims, suspects, witnesses, acquaintances and locations of interest in the investigation such as workplaces or nightclubs. Such diagrammatic representations often provide the focus for discussion among the investigating team and are incrementally added to as new facts are discovered. In this paper we present a brief overview of this important subject area and discuss how such software products could be further enhanced. We also present an example that illustrates the basic principles using a demonstrator we developed.