Sensor network applications frequently require that the sensors know their physical locations in some global coordinate system. This is usually achieved by equipping each sensor with a location measurement device, such as GPS. However, low-end systems or indoor systems, which cannot use GPS, must locate themselves based only on crude information available locally, such as inter-sensor distances. We show how a collection of sensors, capable only of measuring distances to close neighbors, can compute their locations in a purely distributed manner, i.e. where each sensor communicates only with its neighbors. This can be viewed as a distributed graph drawing algorithm. We experimentally show that our algorithm consistently produces good results under a variety of simulated real-world conditions, and is relatively robust to the presence of noise in the distance measurements.

Visualisations implemented as virtual worlds can allow users to comprehend large graphs more e#ectively. Good 3D layout algorithms are an important element. Angle has been developed as a platform for experimenting with 3D force-directed layout algorithms. The big-bang modification is proposed as a means of obtaining e#ciently good 3D layouts for a wide range of graphs. Results are presented and compared with those from a conventional approach. 1

We present an algorithm for drawing directed graphs, which is based on rapidly solving a unique onedimensional optimization problem for each of the axes. The algorithm results in a clear description of the hierarchy structure of the graph. Nodes are not restricted to lie on fixed horizontal layers, resulting in layouts that convey the symmetries of the graph very naturally. The algorithm can be applied without change to cyclic or acyclic digraphs, and even to graphs containing both directed and undirected edges. We also derive a hierarchy index from the input digraph, which quantitatively measures its amount of hierarchy.

We present an algorithm for drawing directed graphs, which is based on rapidly solving a unique one-dimensional optimization problem for each of the axes. The algorithm results in a clear description of the hierarchy structure of the graph. Nodes are not restricted to lie on fixed horizontal layers, resulting in layouts that convey the symmetries of the graph very naturally. The algorithm can be applied without change to cyclic or acyclic digraphs, and even to graphs containing both directed and undirected edges. We also derive a hierarchy index from the input digraph, which quantitatively measures its amount of hierarchy.

In recent years there has been a resurgence of interest in nonlinear dimension reduc-tion methods. Among new proposals are so-called “Local Linear Embedding ” (LLE) and “Isomap”. Both use local neighborhood information to construct a global low-dimensional embedding of a hypothetical manifold near which the data fall. In this paper we introduce a family of new nonlinear dimension reduction methods called “Local Multidimensional Scaling ” or LMDS. Like LLE and Isomap, LMDS only uses local information from user-chosen neighborhoods, but it differs from them in that it uses ideas from the area of “graph layout”. A common paradigm in graph layout is to achieve desirable drawings of graphs by minimizing energy functions that balance attractive forces between near points and repulsive forces between non-near points against each other. We approach the force paradigm by proposing a parametrized family of stress or energy functions inspired by Box-Cox power transformations. This family provides users with considerable flexibility for achieving desirable embeddings, and it comprises most energy functions proposed in the past.

Abstract. The spectral approach for graph visualization computes the layout of a graph using certain eigenvectors of related matrices. Some important advantages of this approach are an ability to compute optimal layouts (according to specific requirements) and a very rapid computation time. In this paper we explore spectral visualization techniques and study their properties from different points of view. We also suggest a novel algorithm for calculating spectral layouts resulting in an extremely fast computation by optimizing the layout within a small vector space.

It has been known for some time that larger graphs can be interpreted if laid out in 3D and displayed with stereo and/or motion depth cues to support spatial perception. However, prior studies were carried out using displays that provided a level of detail far short of what the human visual system is capable of resolving. Therefore we undertook a graph comprehension study using a very high resolution stereoscopic display. In our first experiment we examined the effect of stereo, kinetic depth and using 3D tubes versus lines to display the links. The results showed a much greater benefit for 3D viewing than previous studies. For example, with both motion and depth cues, unskilled observers could see paths between nodes in 333 node graphs with less than a 10 % error rate. Skilled observers could see up to a 1000 node graph with less than a 10 % error rate. This represented an order of magnitude increase over 2D display. In our second experiment we varied both nodes and links to understand the constraints on the number of links and the size of graph that can be reliably traced. We found the difference between number of links and number of nodes to best account for error rates and suggest that this is evidence for a “perceptual phase transition”. These findings are discussed in terms of their implications for information display.

In this paper we describe a unique type of knowledge management systems virtual reality-enabled multi-user virtual environments with spatialised semantic structures. They are designed to enable users to exploit emerging knowledge structures shared among a group of people and engage in social interaction with concurrent users in the virtual world. The design principle is illustrated by an example of how a heterogeneous collection of accumulated documents and user profiles is visualised. Resultant spatial structures reveal not only interdocument relationships, but also the interconnectivity between user profiles and documents.

) F. J. Brandenburg , M. Himsolt, H. J. Roder, and K. Skodinis University of Passau D-94030 Passau Germany fbrandenb,himsolt,roeder,skodinisg@fmi.uni-passau.de ABSTRACT We introduce a new approach to construct data flow graphs of imperative programs. It is based on graphically specified templates rather than on writing code. To each syntactical unit of the program, our technique assigns a fixed set of graph grammar productions. Given a program, the data flow graph is created by the application of productions according to the syntactical structure of the program. We have implemented our approach with the GraphEd system. This allows the design of the graph grammar on screen and to generate a visual representation of the data flow graph automatically from a given program. 1 Introduction Data flow graphs are used for the analysis of programs in compiler construction or as a basis for data flow computer architectures. In a data flow graph, nodes represent operations and edges model ...

. LayoutShow is a Java-based multi-threaded applet/application for experimentation with graph drawing algorithms, particularly, forcedirected algorithms. The motivation behind the development of this software is the lack of features that would help to experiment, and as a result, understand the behavior of force-directed algorithms in the existing graph drawing software. Some of these features include smooth node-based and iteration-based animations, display of running-time and iteration counts, and variety of initial layout algorithms. LayoutShow supports a number of force-directed graph drawing algorithms as well as layouts based on eigenvectors. Node-based and iteration-based animations have been implemented. In addition, the software provides some algorithms for producing non-random initial layouts for force-directed algorithms. File I/O using GML le format has been implemented. Furthermore, users of LayoutShow applet can choose to perform local le I/O since LayoutS...