Graph layout using subgraph isomorphisms

Today, graphs are used for many things. In engineering, graphs are used to design circuits in very large scale integration. In computer science, graphs are used in the representation of the structure of software. They show information such as the flow of data through the program (known as the data flow graph [1]) or the information about the calling sequence of programs (known as the call graph [145]). These graphs consist of many classes of graphs and may occupy a large area and involve a large number of vertices and edges. The manual layout of graphs is a tedious and error prone task. Algorithms for graph layout exist but tend to only produce a 'good' layout when they are applied to specific classes of small graphs. In this thesis, research is presented into a new automatic graph layout technique. Within many graphs, common structures exist. These are structures that produce 'good' layouts that are instantly recognisable and, when combined, can be used to improve the layout of the graphs. In this thesis common structures are given that are present in call graphs. A method of using subgraph isomorphism to detect these common structures is also presented. The method is known as the ANHOF method. This method is implemented in the ANHOF system, and is used to improve the layout of call graphs. The resulting layouts are an improvement over layouts from other algorithms because these common structures are evident and the number of edge crossings, clusters and aspect ratio are improved

Experimental and Theoretical Results in Interactive Orthogonal Graph Drawing

Interactive Graph Drawing allows the user to dynamically interact with a drawing as the design progresses while preserving the user's mental map. This paper presents a theoretical analysis of Relative-Coordinates and an extensive experimental study comparing the performance of two interactive orthogonal graph drawing scenaria: No-Change, and Relative-Coordinates. Our theoretical analysis found that the Relative-Coordinates scenario builds a drawing that has no more than 3n-1 bends, while the area of the drawing is never larger than 2.25n². Also, no edge has more than 3 bends at any time during the drawing process. To conduct the expirements, we used a large set of test data consisting of 11,491 graphs (ranking from 6 to 100 nodes) and compared the behavior of the above two scenaria with respect to various aesthetic properties (e.g., area, bends, crossings, edge length, etc.) of the corresponding drawings. The Relative-Coordinates scenario was a winner over No-change under any aesthetic measure considered in our experiments. Moreover, the practical behavior of the two scenaria was considerably better than the established theoretical bounds, in most cases

Experimental and Theoretical Results in Interactive Orthogonal Graph Drawing

. Interactive Graph Drawing allows the user to dynamically interact with a drawing as the design progresses while preserving the user's mental map. This paper presents a theoretical analysis of RelativeCoordinates and an extensive experimental study comparing the performance of two interactive orthogonal graph drawing scenaria: No-Change, and Relative-Coordinates.Our theoretical analysis found that the RelativeCoordinates scenario builds a drawing that has no more than 3n \Gamma 1 bends, while the area of the drawing is never larger than 2:25n 2 . Also, no edge has more than 3 bends at any time during the drawing process. To conduct the experiments, we used a large set of test data consisting of 11,491 graphs (ranging from 6 to 100 nodes) and compared the behavior of the above two scenaria with respect to various aesthetic properties (e.g., area, bends, crossings, edge length, etc) of the corresponding drawings. The Relative-Coordinates scenario was a winner over No-Change under any..