-
[show abstract]
[hide abstract]
ABSTRACT: Given a graph G=(V,E) and two vertices s,t ∈ V , s\neq t , the Menger problem is to find a maximum number of disjoint paths connecting s and t . Depending on whether the input graph is directed or not, and what kind of disjointness criterion is demanded, this general
formulation is specialized to the directed or undirected vertex, and the edge or arc disjoint Menger problem, respectively.
For planar graphs the edge disjoint Menger problem has been solved to optimality [W2], while the fastest algorithm for the
arc disjoint version is Weihe's general maximum flow algorithm for planar networks [W1], which has running time \bf O (|V| log |V|) . Here we present a linear time, i.e., asymptotically optimal, algorithm for the arc disjoint version in planar directed
graphs.
Key words. Graph algorithms, Disjoint paths, Planar graphs.
Algorithmica 04/2012; 28(1):16-36. · 0.60 Impact Factor
-
[show abstract]
[hide abstract]
ABSTRACT: 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.
Visualization Symposium, 2008. PacificVIS '08. IEEE Pacific; 04/2008
-
[show abstract]
[hide abstract]
ABSTRACT: We augment schematic maps of transportation systems by superimposing them on street-level maps that are fitted using image warping techniques. While schematic maps are successful in conveying information about lines and connections in a public transportation network, they usually contain little or no detail describing the environment of stations or their embedding in the surrounding area. The annotation of a distorted city map therefore alleviates this deficiency and improves further the usability of schematic transportation maps by merging two different navigational spaces. Our technique for fitting the street map to the schematic map is based on moving least squares in combination with an overlap control technique. We thus obtain an easily readable transportation network map on which we can show all the typical city map features such as rivers, streets, and parks without compromising on the schematization. Furthermore, for the interactive exploration we couple zooming with warping and control over the level of detail in what we call warping zoom.
Visualization Symposium, 2008. PacificVIS '08. IEEE Pacific; 04/2008
-
[show abstract]
[hide abstract]
ABSTRACT: Modularity is a recently introduced quality measure for graph clusterings. It has immediately received considerable attention in several disciplines, particularly in the complex systems literature, although its properties are not well understood. We study the problem of finding clusterings with maximum modularity, thus providing theoretical foundations for past and present work based on this measure. More precisely, we prove the conjectured hardness of maximizing modularity both in the general case and with the restriction to cuts and give an Integer Linear Programming formulation. This is complemented by first insights into the behavior and performance of the commonly applied greedy agglomerative approach.
IEEE Transactions on Knowledge and Data Engineering 03/2008; · 1.66 Impact Factor
-
[show abstract]
[hide abstract]
ABSTRACT: We consider routing methods for networks when geographic positions of nodes are available. Instead of using the original geographic coordinates, however, we precompute virtual coordinates using a barycentric layout. Combined with simple geometric routing rules, this greatly reduces the lengths of routes and outperforms algorithms working on the original coordinates. Along with experimental results we proof properties such as guaranteed message delivery and worst-case optimality. Our methods apply to static networks in which short routes are important, but memory for full routing tables is not available and the one-time-precomputation is affordable.
Information Visualization, 2007. IV '07. 11th International Conference; 08/2007
-
[show abstract]
[hide abstract]
ABSTRACT: Several algorithms have been proposed to compute partitions of networks into communities that score high on a graph clustering index called modularity. While publications on these algorithms typically contain experimental evaluations to emphasize the plausibility of results, none of these algorithms has been shown to actually compute optimal partitions. We here settle the unknown complexity status of modularity maximization by showing that the corresponding decision version is NP-complete in the strong sense. As a consequence, any efficient, i.e. polynomial-time, algorithm is only heuristic and yields suboptimal partitions on many instances.
09/2006;
-
[show abstract]
[hide abstract]
ABSTRACT: We present a method for visual summary of bilateral conflict structures embodied in event data. Such data consists of actors linked by time stamped events, and may be extracted from various sources such as news reports and dossiers. When analyzing political events, it is of particular importance to be able to recognize conflicts and actors involved in them. By projecting actors into a conflict space, we are able to highlight the main opponents in a series of tens of thousands of events, and provide a graphic overview of the conflict structure. Moreover, our method allows for smooth animation of the dynamics of a conflict.
Information Visualization, 2005. INFOVIS 2005. IEEE Symposium on; 11/2005
-
[show abstract]
[hide abstract]
ABSTRACT: A new method for visualizing the class of incrementally evolving networks is presented. In addition to the intermediate states of the network it conveys the nature of the change between them by unrolling the dynamics of the network. Each modification is shown in a separate layer of a three-dimensional representation, where the stack of layers corresponds to a time line of the evolution. We focus on discourse networks as the driving application, but our method extends to any type of network evolving in similar ways.
Information Visualization, 2002. INFOVIS 2002. IEEE Symposium on; 02/2002
-
[show abstract]
[hide abstract]
ABSTRACT: Wikipedia is a large and rapidly growing Web-based collaborative authoring environment, where anyone on the Internet can create, modify, and delete pages about encyclopedic topics. A remarkable property of some Wikipedia pages is that they are written by up to thousands of authors who may have contradicting opinions. In this paper we show that a visual analysis of the "who revises whom"- network gives deep insight into controversies. We propose a set of analysis and visualization techniques that reveal the dominant authors of a page, the roles they play, and the alters they confront. Thereby we provide tools to understand how Wikipedia authors collaborate in the presence of controversy.
Visual Analytics Science and Technology, 2007. VAST 2007. IEEE Symposium on;
