The analysis of large graphs plays a prominent role in various fields of research and is relevant in many important application areas. Effective visual analysis of graphs requires appropriate visual presentations in combination with respective user interaction facilities and algorithmic graph analysis methods. How to design appropriate graph analysis systems depends on many factors, including the type of graph describing the data, the analytical task at hand and the applicability of graph analysis methods. The most recent surveys of graph visualization and navigation techniques cover techniques that had been introduced until 2000 or concentrate only on graph layouts published until 2002. Recently, new techniques have been developed covering a broader range of graph types, such as timevarying graphs. Also, in accordance with ever growing amounts of graph-structured data becoming available, the inclusion of algorithmic graph analysis and interaction techniques becomes increasingly important. In this State-of-the-Art Report, we survey available techniques for the visual analysis of large graphs. Our review first considers graph visualization techniques according to the type of graphs supported. The visualization techniques form the basis for the presentation of interaction approaches suitable for visual graph exploration. As an important component of visual graph analysis, we discuss various graph algorithmic aspects useful for the different stages of the visual graph analysis process. We also present main open research challenges in this field.

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Visual analysis of large graphs : state-of-the-art and future research challenges

Today's technical and legal landscape presents formidable challenges to personal data privacy First, our increasing reliance on Web services causes personal data to be cached, copied, and archived by third parties, often without our knowledge or control Second, the disclosure of private data has become commonplace due to carelessness, theft, or legal actions

Our research seeks to protect the privacy of past, archived data -- such as copies of emails maintained by an email provider -- against accidental, malicious, and legal attacks Specifically, we wish to ensure that all copies of certain data become unreadable after a userspecified time, without any specific action on the part of a user, and even if an attacker obtains both a cached copy of that data and the user's cryptographic keys and passwords

This paper presents Vanish, a system that meets this challenge through a novel integration of cryptographic techniques with global-scale, P2P, distributed hash tables (DHTs) We implemented a proof-of-concept Vanish prototype to use both the million-plus-node Vuze Bit-Torrent DHT and the restricted-membership OpenDHT We evaluate experimentally and analytically the functionality, security, and performance properties of Vanish, demonstrating that it is practical to use and meets the privacy-preserving goals described above We also describe two applications that we prototyped on Vanish: a Firefox plugin for Gmail and other Web sites and a Vanishing File application

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Vanish: increasing data privacy with self-destructing data

In this paper, we describe a taxonomy of generic graph related tasks and an evaluation aiming at assessing the readability of two representations of graphs: matrix-based representations and node-link diagrams. This evaluation bears on seven generic tasks and leads to important recommendations with regard to the representation of graphs according to their size and density. For instance, we show that when graphs are bigger than twenty vertices, the matrix-based visualization performs better than node-link diagrams on most tasks. Only path finding is consistently in favor of node-link diagrams throughout the evaluation

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A Comparison of the Readability of Graphs Using Node-Link and Matrix-Based Representations

In this article, we describe a taxonomy of generic graph related tasks along with a computer-based evaluation designed to assess the readability of two representations of graphs: matrix-based representations and node-link diagrams. This evaluation encompasses seven generic tasks and leads to insightful recommendations for the representation of graphs according to their size and density. Typically, we show that when graphs are bigger than twenty vertices, the matrix-based visualization outperforms node-link diagrams on most tasks. Only path finding is consistently in favor of node-link diagrams throughout the evaluation.

On the readability of graphs using node-link and matrix-based representations: a controlled experiment and statistical analysis

We introduce a new method to optimize the required area, minimum angle, and number of bends of planar graph drawings on a grid. The main tool is a new type of ordering on the vertices and faces of triconnected planar graphs. Using this method linear-time-and-space algorithms can be designed for many graph-drawing problems. Our main results are as follows:


Every triconnected planar graphG admits a planar convex grid drawing with straight lines on a (2n−4)×(n−2) grid, wheren is the number of vertices.


Every triconnected planar graph with maximum degree 4 admits a planar orthogonal grid drawing on ann×n grid with at most [3n/2]+4 bends, and ifn>6, then every edge has at most two bends.


Every planar graph with maximum degree 3 admits a planar orthogonal grid drawing with at most [n/2]+1 bends on an [n/2]×[n/2] grid.


Every triconnected planar graphG admits a planar polyline grid drawing on a (2n−6)×(3n−9) grid with minimum angle larger than 2/d radians and at most 5n−15 bends, withd the maximum degree.

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Drawing planar graphs using the canonical ordering

In Crypto '95, Micali and Sidney proposed a method for shared generation of a pseudo-random function f(ċ) among n players in such a way that for all the inputs x, any u players can compute f(x) while t or fewer players fail to do so, where 0 ≤ t < u ≤ n. The idea behind the Micali-Sidney scheme is to generate and distribute secret seeds S = {s1, ..., sd} of a poly-random collection of functions, among the n players, each player gets a subset of S, in such a way that any u players together hold all the secret seeds in S while any t or fewer players will lack at least one element from S. The pseudo-random function is then computed as f(x) = ⊕i=1d fsi (x), where fsi (ċ)'s are poly-random functions. One question raised by Micali and Sidney is how to distribute the secret seeds satisfying the above condition such that the number of seeds, d, is as small as possible. In this paper, we continue the work of Micali and Sidney.We first provide a general framework for shared generation of pseudo-random function using cumulative maps. We demonstrate that the Micali-Sidney scheme is a special case of this general construction.We then derive an upper and a lower bound for d. Finally we give a simple, yet efficient, approximation greedy algorithm for generating the secret seeds S in which d is close to the optimum by a factor of at most u ln 2.

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Authenticated data structures for graph and geometric searching

Drawing graphs is an important problem that combines elements of computational geometry and graph theory. Applications can be found in a variety of areas including circuit layout, network management, software engineering, and graphics. 
The main contributions of this paper can be summarized as follows: 
We devise a model for dynamic graph algorithms, based on performing queries and updates on an implicit representation of the drawing, and we show its applications. 
We present efficient dynamic drawing algorithms for trees and series-parallel digraphs. 
As further applications of the model, we give dynamic drawing algorithms for planar st-digraphs and planar graphs. Our algorithms adopt a variety of representations (e.g., straight line, polyline, visibility) and update the drawing in a smooth way.

Dynamic Graph Drawings: Trees, Series-Parallel Digraphs, and Planar ST -Digraphs

In this paper we give a model for dynamic graph algorithms, based on performing queries and updates on an implicit representation of the drawing. We present dynamic algorithms for drawing planar graphs that use a variety of drawing standards (such as polyline, straight-line, orthogonal, grid, upward, and visibility drawings), and address aesthetic criteria that are important for readability, such as the display of planarity, symmetry, and reachability. Also, we provide techniques that are especially tailored for important subclasses of planar graphs such as trees and series-parallel digraphs. Our dynamic drawing algorithms have the important property of performing “smooth updates” of the drawing. Of special geometric interest is the possibility of performing point-location and window queries on the implicit representation of the drawing.

A framework for dynamic graph drawing

We present a technique for dynamically maintaining a collection of arithmetic expressions represented by binary trees (whose leaves are variables and whose internal nodes are operators). A query operation asks for the vahre of an expression (associated with the root of a tree). Update operations include changing the value of a variable and combining or decomposing expressions by linking or cutting the corresponding trees. Our dynamic data structure uses linear space and supports queries and updates in logarithmic time. An important application is the dynamic maintenance of maximum flow and shortest path in series-parallel digraphs under a sequence of vertex and edge insertions, series and parallel compositions, and their respective inverses. Queries include reporting the maximum flow or shortest st-path in a series-parallel subgraph.

Dynamic expression trees and their applications

We present our ongoing research in the communication of graphs and relational information to blind computer science students. We have developed a system called exPLoring graphs at UMB (PLUMB) that displays a drawn graph on a tablet PC and uses auditory cues to help a blind user navigate the graph. Beyond Computer Science education, this work has applications to assist blind individuals in navigation, map manipulation and other applications that require graph visualization.

Robert F. Cohen

Papers

Authenticated data structures for graph and geometric searching

Dynamic Graph Drawings: Trees, Series-Parallel Digraphs, and Planar ST -Digraphs

A framework for dynamic graph drawing

Dynamic expression trees and their applications

Teaching graphs to visually impaired students using an active auditory interface