Aggregation and other patterns of graphs in space.
Degree GrantorUniversity of Canterbury
Degree NameDoctor of Philosophy
Space as perceived by humans may be described by 2-D space, 3-D space, or 4-D space, which includes the temporal dimension. Within the space that is most commonly used, the urban space, there exists an even more specialised space, the graph space. This work develops techniques for the representation of these graphs in space. The representation of geographic space needs to satisfy some recurring patterns of requirements, such as capturing topology, multiple representations and spatial indexing for fast access. These three requirements for representing the graph space have been addressed in this work. The main contribution of this work is in the multiple representation of the graph space, which is addressed as a graph aggregation problem. This graph aggregation is based on some ordered values associated with the edges of the graph and can be defined without any other information except this edge attribute. This permits a very simple means of achieving graph aggregation and also facilitates a simple user interface for defining it. Graph aggregation is applied to transportation networks to improve any shortest path algorithm. Application of the proposal in spatial interaction modelling is also suggested. The proposal in this work is a specific interpretation of graph aggregation and is compared with similar schemes. Capture of the topology of spatial objects in 2-D space has been investigated extensively by researchers. A simplified model for capturing the topology of extensible graph space has been developed. An Rtree based indexing scheme is also developed for indexing this extensible graph space, which can be used to implement an interactive brows able view. Two user interface software patterns for developing such browsable 2-D views are also presented.