On labeling in graph visualization

When visualizing graphs, it is essential to communicate the meaning of each graph object via text or graphical labels. Automatic placement of labels in a graph is an NP-Hard problem, for which efficient heuristic solutions have been recently developed. In this paper, we describe a general framework for modeling, drawing, editing, and automatic placement of labels respecting user constraints. In addition, we present the interface and the basic engine of the Graph Editor Toolkit - a family of portable graph visualization libraries designed for integration into graphical user interface application programs. This toolkit produces a high quality automated placement of labels in a graph using our framework. A brief survey of automatic label placement algorithms is also presented. Finally we describe extensions to certain existing automatic label placement algorithms, allowing their integration into this visualization tool. © 2007 Elsevier Inc. All rights reserved

Automatic Visualization of Software Requirements: Reactive Systems

In this paper we present an approach that facilitates the validation of high consequence system requirements. This approach consists of automatically generating a graphical representation from an informal document. Our choice of a graphical notation is statecharts. We proceed in two steps: we first extract a hierarchical decomposition tree from a textual description, then we draw a graph that models the statechart in a hierarchical fashion. The resulting drawing is an effective requirements assessment tool that allows the end user to easily pinpoint inconsistencies and incompleteness

Connected rectilinear graphs on point sets

Given n points in d-dimensional space, we would like to connect the points with straight line segments to form a connected graph whose edges use d pairwise perpendicular directions. We prove that there exists at most one such set of directions. For d¿=¿2 we present an algorithm for computing these directions (if they exist) in O (n 2) time

Drawing (complete) binary tanglegrams: Hardness, approximation, fixed-parameter tractability

A binary tanglegram is a pair 〈S, T 〉 of binary trees whose leaf sets are in one-to-one correspondence; matching leaves are connected by inter-tree edges. For applications, for example in phylogenetics, it is essential that both trees are drawn without edge crossings and that the inter-tree edges have as few crossings as possible. It is known that finding a drawing with the minimum number of crossings is NP-hard and that the problem is fixed-parameter tractable with respect to that number. We prove that under the Unique Games Conjecture there is no constantfactor approximation for general binary trees. We show that the problem is hard even if both trees are complete binary trees. For this case we give an O(n³)-time 2-approximation and a new and simple fixed-parameter algorithm. We show that the maximization version of the dual problem for general binary trees can be reduced to a version of MaxCut for which the algorithm of Goemans and Williamson yields a 0.878-approximation