Algorithm Visualization System for Teaching Spatial Data Algorithms

Introduction Spatial data is data that is located in a multidimensional space (Laurini & Thompson, 1992). In other words, each spatial data item is identified by a set of coordinates, which define its location in relation to other data items. Thus, each spatial data item contains spatial information (coordinates) that describes the location of the item and associated attribute data that describes what it represents. Spatial data is used in numerous disciplines, such as geographic information systems (GIS), computer graphics, robotics, virtual reality, computer-aided design, biology, VLSI design, and many others. In the context of GIS and related disciplines, the data is assumed to model geographic locations on the Earth's surface and their associated properties. In this paper, we discuss spatial data in this context. In GIS, there are at least two coordinate axes (x and y, which represent geographical longitude and latitude), and two additional ones (height and time) can also be used. Spatial data algorithms (SDA) are algorithms designed to process and manipulate such data and spatial data structures are entities used to store the data. Spatial data structures are based on regular non-spatial data structures such as arrays and trees, as well as algorithms that manipulate these basic structures. However, the multidimensional nature of spatial data makes them more complex than the basic data structures. This also makes the design and implementation of efficient spatial data algorithms more difficult. For example, dictionary structures for spatial data must be able to locate data items according to their coordinates instead of using one-dimensional key values. Furthermore, the spatial nature of the data makes teaching spatial data algorithms more challenging than basic non-spatial data structures and algorithms. For example, in order to show both how data items are related to each other and how they are arranged in a data structure, typically two illustrations are required: one to show the data items and the space they occupy, and another to show the data structures. Consequently, the learner must be able to connect the illustrations in order to comprehend how the data is organized. In basic data structures, on the other hand, the relationships between the data items are typically distinguishable with just a single picture. SDA and associated data structures are an integral part of geoinformatics, a branch of science where computer science is applied to cartography and geosciences. The data geoinformatics studies is location data on the Earth's surface, and therefore SDA are required for efficient storage and processing. Geoinformatics is also closely related to cartography, and therefore many different kinds of illustrations are used. Maps are the most fundamental way to represent spatial information. Visualization of maps is in itself a large, varied and important field (Slocum, McMaster, Kessler, & Howard, 2004). However, since many spatial data sets have several properties for each location, other visualization methods are also required for understanding the data. For example, multivariate visualization techniques such as parallel coordinate plots or star plots can be used in conjunction with map views. A map view shows how the data is distributed geographically, while other views show what information the data contains. Software Visualization (SV) is a branch of software engineering that aims to use graphics and animation to illustrate the different aspects of software (Stasko, Domingue, Brown, & Price, 1998). Price, Baecker, and Small (1993) divide SV into two subcategories: program visualization (PV) and algorithm visualization (AV). PV is the use of various visual techniques to enhance the human understanding of computer programs. It is typically used to illustrate actual, implemented programs. AV, on the other hand, illustrates abstractions of algorithmic concepts and is independent of any actual algorithm implementation. …