Dominance Drawing of Non-Planar Graphs

In information technology, big data is a term used to describe data sets so large and complex that they become awkward to work and analyze. Difficulties include capture, storage, search, sharing, analysis, and visualization. In this work we focus in the latter part, specifically we study the visualization of graphs. The need for simple and intuitive visualization techniques is more imminent than ever. In this thesis we propose a new framework for visualizing graphs. We extend the so-called Dominance Drawing method, by relaxing some constraints in order to include the much broader family of directed acyclic graphs. We introduce a new computational problem called Weak Dominance Placement, which we prove NPcomplete using notions from the field of Order Theory. We offer simple bounds and properties as well as three heuristic algorithms in order to obtain locally optimal solutions. Using a weak dominance placement of the vertices, we propose a new graph drawing model for visualizing directed acyclic graphs called Overloaded Orthogonal. In order to simplify our drawings we use an overloading technique for edge routing. All algorithms are simple and easy to implement and can be applied to directed acyclic graphs of arbitrary degree, planar, and non-planar graphs. We also present bounds on the number of bends and the layout area of a graph. Overloaded Orthogonal drawings present several interesting properties such as efficient visual edge confirmation as well as simplicity and clarity of the drawing. Furthermore, we propose the DAGView framework which handles not only directed acyclic graphs, but also graphs with cycles and undirected graphs. Our approach combines the readability and scalability of a matrix based approach, with the intuitiveness of a node-link approach in spotting a node within the layout and in following an edge to find its destination. We have implemented the DAGView framework in Java and the results are very encouraging. Finally, we believe that DAGView visualizations will be well accepted in user studies, since several criteria that users identified as important in a layout are met: underlying grid, crossings that appear perpendicular, easy check for the existence of an edge and/or path, preservation of the mental-map.