This is a survey on graph visualization and navigation techniques, as used in information visualization. Graphs appear in numerous applications such as web browsing, state--transition diagrams, and data structures. The ability to visualize and to navigate in these potentially large, abstract graphs is often a crucial part of an application. Information visualization has specific requirements, which means that this survey approaches the results of traditional graph drawing from a different perspective. Index Terms---Information visualization, graph visualization, graph drawing, navigation, focus+context, fish--eye, clustering. 1

We describe a package of practical tools and libraries for manipulating graphs and their drawings. Our design, which aimed at facilitating the combination of the package components with other tools, includes stream and event interfaces for graph operations, high-quality static and dynamic layout algorithms, and the ability to handle sizable graphs. We conclude with a description of the applications of this package to a variety of software engineering tools.

This paper describes the Oz Explorer and its implementation. The Explorer is a visual constraint programming tool intended to support the development of constraint programs. It uses the search tree of a constraint problem as its central metaphor. Exploration and visualization of the search tree are userdriven and interactive. The constraints of any node in the tree are available first-class: predefined or user-defined procedures can be used to display or analyze them. The Explorer is a fast and memory efficient tool intended for the development of real-world constraint programs. The Explorer is implemented in Oz using first-class computation spaces. There is no fixed search strategy in Oz. Instead, first-class computation spaces allow to program search engines. The Explorer is one particular example of a user-guided search engine. The use of recomputation to trade space for time makes it possible to solve large real-world problems, which would use too much memory otherwise.

KIV is a tool for formal systems development. It can be employed, e.g., – for the development of safety critical systems from formal requirements specifications to executable code, including the verification of safety requirements and the correctness of implementations, – for semantical foundations of programming languages from a specification of the semantics to a verified compiler, – for building security models and architectural models as they are needed for high level ITSEC [7] or CC [1] evaluations. Special care was (and is) taken to provide strong proof support for all validation and verification tasks. KIV can handle large scale formal models by efficient proof techniques, multi-user support, and an ergonomical user interface. It has been used in a number of industrial pilot applications, but is also useful as an educational tool for formal methods courses. Details on KIV can be found in [9] [10] [11] and under http://www.informatik.uni-ulm.de/pm/kiv/.

. We demonstrate the H3Viewer graph drawing library, which can be run from a standalone program or in conjunction with other programs such as SGI's Site Manager application. Our layout and drawing algorithms support interactive navigation of large graphs up to 100,000 edges. We present an adaptive drawing algorithm with a guaranteed frame rate. Both layout and navigation occur in 3D hyperbolic space, which provides a view of a large neighborhood around an easily changeable point of interest. We find an appropriate spanning tree to use as the backbone for fast layout and uncluttered drawing, and non-tree links can be displayed on demand. Our methods are appropriate when node or link annotations can guide the choice of a good parent from among all of the incoming links. Such annotations can be constructed using only a small amount of domain-specific knowledge, thus rendering tractable many graphs which may seem rather densely connected at first glance. 1 Motivation and Context Software s...

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Words that are, by some measure, over- or underrepresented in the context of larger sequences have been variously implicated in biological functions and mechanisms. In most approaches to such anomaly detections, the words (up to a certain length) are enumerated more or less exhaustively and are individually checked in terms of observed and expected frequencies, variances, and scores of discrepancy and significance thereof. Here we take the global approach of annotating the suffix tree of a sequence with some such values and scores, having in mind to use it as a collective detector of all unexpected behaviors, or perhaps just as a preliminary filter for words suspicious enough to undergo a more accurate scrutiny. We consider in depth the simple probabilistic model in which sequences are produced by a random source emitting symbols from a known alphabet independently and according to a given distribution. Our main result consists of showing that, within this model, full tree annotations can be carried out in a time-and-space optimal fashion for the mean, variance and some of the adopted measures of significance. This result is achieved by an ad hoc embedding in statistical expressions of the combinatorial structure of the periods of a string. Specifically,

and Demo) Michael Himsolt Universitat Passau, 94032 Passau, GERMANY himsolt@fmi.uni-passau.de Abstract. GraphEd is an extensible graph editor. Its powerful object oriented user interface supports all operations that are necessary for the convenient construction and manipulation of graphs. Graph grammars can be used as a macro system to create structured graphs. GraphEd's modular structure and the application interface support the easy integration of algorithm modules which are written in C, or can run external programs. The user may construct graphs interactively, select algorithms from a menu, and view the results of an algorithm directly on screen. Several graph layout algorithms assist the user to tidy graph drawings, and help the programmer to visualize results or debug complex algorithms. Actual applications range from standard graph algorithms over graph drawing algorithms, algorithm animation and combinatorial algorithms to front ends for circuit design systems. 1 Introduction...

Abstract—We describe ASK-GraphView, a node-link-based graph visualization system that allows clustering and interactive navigation of large graphs, ranging in size up to 16 million edges. The system uses a scalable architecture and a series of increasingly sophisticated clustering algorithms to construct a hierarchy on an arbitrary, weighted undirected input graph. By lowering the interactivity requirements we can scale to substantially bigger graphs. The user is allowed to navigate this hierarchy in a top down manner by interactively expanding individual clusters. ASK-GraphView also provides facilities for filtering and coloring, annotation and cluster labeling. Index Terms — Information Visualization, Graph Visualization, Graph Clustering. 1

The aim of this chapter is to describe the integrated specification- and theorem proving environment of KIV. KIV is an advanced tool for developing high assurance systems. It supports: --- hierarchical formal specification of software and system designs --- specification of safety/security models --- proving properties of specifications --- modular implementation of specification components --- modular verification of implementations --- incremental verification and error correction --- reuse of specifications, proofs, and verified components KIV supports the entire design process from formal specifications to verified code. It supports functional as well as state-based modeling. KIV is ready for use, and has been tested in a number of indu...