Foundation (JU204/10-1). Abstract. We study the problem of simultaneously embedding several graphs on the same vertex set in such a way that edges common to two or more graphs are represented by the same curve. This problem is known as simultaneously embedding graphs with fixed edges. We show that this problem is closely related to the weak realizability problem: Can a graph be drawn such that all edge crossings occur in a given set of edge pairs? By exploiting this relationship we can explain why the simultaneous embedding problem is challenging, both from a computational and a combinatorial point of view. More precisely, we prove that simultaneously embedding graphs with fixed edges is NP-complete even for three planar graphs. For two planar graphs the complexity status is still open. 1

We propose a method to visually summarize collections of networks on which a clustering of the vertices is given. Our method allows for efficient comparison of individual networks, as well as for visualizing the average composition and structure of a set of networks. As a concrete application we analyze a set of several hundred personal networks of migrants. On the individual level the network images provide visual hints for assessing the mode of acculturation of the respondent. On the population level they show how cultural integration varies with specific characteristics of the migrants such as country of origin, years of residence, or skin color.

The augmented desk is gaining popularity in recent HCI research. Its layout of a large horizontal screen on the desk enhances immersive and intense collaborative experiences. A responsive and unimpeded input interface is important for an efficient interaction in such an environment. In this paper, we developed a real-time stereo vision-based finger pointing interface for our augmented desk that supports drag-and-drop operation by the tap-and-move of the index finger. The core of our system is a 3D fingertip tracking system, which requires both careful calibration and efficient fingertip localization algorithm. To meet these requirements, we have designed a two-step calibration method that strikes a good balance between accuracy and convenience. Furthermore, based on the chain code representation of the contour, we propose the direction cancellation vector as a tool for fingertip localization. Our algorithm works efficiently with a time complexity of O (n) in term of the length of the chain code. Currently our system allows a user to select and move the displayed contents on the screen directly using his fingertip, and it is applied to the interactive graph drawing paradigm proposed by do Nascimento and Eades (2001). In this application, our real-time pointing interface enables the user to interact with a graph drawing program dynamically, which results in optimal layouts of graphs with maximum symmetry. In the last section, the strength and weakness of our system are discussed, and further suggestions to improve the system are also given..

Problems in simultaneous graph drawing involve the layout of several graphs on a shared vertex set. This paper describes a Graph Simultaneous Embedding Tool, GraphSET, designed to allow the investigation of a wide range of embedding problems. GraphSET can be used in the study of several variants of simultaneous embedding including simultaneous geometric embedding, simultaneous embedding with fixed edges and colored simultaneous embedding with the vertex set partitioned into color classes. The tool has two primary uses: (i) studying theoretical problems in simultaneous graph drawing through the production of examples and counterexamples and (ii) producing layouts of given classes of graphs using built-in implementations of known algorithms. GraphSET along with movies illustrating its utility are available at

Web site traffic analysis studies how different pages forming Web sites are accessed by their target audience over time. From a business intelligence point of view, it represents one of the key activities for many private companies and public institutions. Recent papers pointed out that Web site traffic analysis is especially useful if it focuses on the user interest into the relevant concepts described in a Web site rather than counting user accesses to the distinct pages forming the Web site. This paper extends existing measures of conceptual Web site traffic analysis and describes a new system that supports this analysis by means of graph visualization techniques. The graph drawing engine of the system is a force-directed heuristic that computes a simultaneous embedding of two suitably defined graphs, that are non-planar in general. The heuristic is especially designed to take into account two important aesthetic criteria of the drawing: crossing resolution and geodesic edge tendency. We also present some experiments and case studies to show the effectiveness of the proposed approach in practice. Submitted:

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