Arlind Nocaj

Organizing Search Results with a Reference Map

We propose a method to highlight query hits in hierarchically clustered collections of interrelated items such as digital libraries or knowledge bases. The method is based on the idea that organizing search results similarly to their arrangement on a fixed reference map facilitates orientation and assessment by preserving a users mental map. Here, the reference map is built from an MDS layout of the items in a Voronoi treemap representing their hierarchical clustering, and we use techniques from dynamic graph layout to align query results with the map. The approach is illustrated on an archive of newspaper articles.

Computing Voronoi Treemaps: Faster, Simpler, and Resolution-independent

Voronoi treemaps represent hierarchies as nested polygons. We here show that, contrary to the apparent popular belief, utilization of an algorithm for weighted Voronoi diagrams is not only feasible, but also more efficient than previous low‐resolution approximations, even when the latter are implemented on graphics hardware. More precisely, we propose an instantiation of Lloyds method for centroidal Voronoi diagrams with Aurenhammers algorithm for power diagrams that yields an algorithm running in 𝒪(n log n) rather than Ω(n2) time per iteration, with n the number of sites. We describe its implementation and present evidence that it is faster also in practice.

Untangling the Hairballs of Multi-Centered, Small-World Online Social Media Networks

Small-world graphs have characteristically low average distance and thus cause force-directed methods to generate drawings that look like hairballs. This is by design as the inherent objective of these methods is a globally uniform edge length or, more generally, accurate distance representation. The problem arises, for instance, with graphs of high density or high conductance, or in the presence of high-degree vertices, all of which tend to pull vertices together and thus result in clutter overspreading variation in local density. We here propose a method specifically for a class of small-world graphs that are typical for online social networks. The method is based on a spanning subgraph that is sparse but connected and consists of strong ties holding together communities. To identify these ties we propose a novel criterion for structural embeddedness. It is based on a weighted accumulation of triangles in quadrangles and can be determined efficiently. An evaluation on empirical and generated networks indicates that our approach improves upon previous methods using other edge indices. Although primarily designed to achieve more informative drawings, our spanning subgraph may also serve as a sparsifier that trims a small-world graph prior to the application of a clustering algorithm. Submitted: November 2014 Reviewed: September 2015 Revised: September 2015 Accepted: September 2015 Final: September 2015 Published: November 2015 Article type: Regular paper Communicated by: C. Duncan and A. Symvonis This research was supported by DFG under grants GRK 1042, Br 2158/6-1, and Br 2158/11-1. The proposed method is available in visone. E-mail addresses: Arlind.Nocaj@uni-konstanz.de (Arlind Nocaj) Mark.Ortmann@uni-konstanz.de (Mark Ortmann) Ulrik.Brandes@uni-konstanz.de (Ulrik Brandes) Konstanzer Online-Publikations-System (KOPS) URL: http://nbn-resolving.de/urn:nbn:de:bsz:352-0-311019 Erschienen in: Journal of Graph Algorithms and Applications : JGAA ; 19 (2015), 2. S. 595-618 https://dx.doi.org/10.7155/jgaa.00370

Probabilistic Graph Layout for Uncertain Network Visualization

We present a novel uncertain network visualization technique based on node-link diagrams. Nodes expand spatially in our probabilistic graph layout, depending on the underlying probability distributions of edges. The visualization is created by computing a two-dimensional graph embedding that combines samples from the probabilistic graph. A Monte Carlo process is used to decompose a probabilistic graph into its possible instances and to continue with our graph layout technique. Splatting and edge bundling are used to visualize point clouds and network topology. The results provide insights into probability distributions for the entire network-not only for individual nodes and edges. We validate our approach using three data sets that represent a wide range of network types: synthetic data, protein-protein interactions from the STRING database, and travel times extracted from Google Maps. Our approach reveals general limitations of the force-directed layout and allows the user to recognize that some nodes of the graph are at a specific position just by chance.

Stub Bundling and Confluent Spirals for Geographic Networks

Edge bundling is a technique to reduce clutter by routing parts of several edges along a shared path. In particular, it is used for visualization of geographic networks where vertices have fixed coordinates. Two main drawbacks of the common approach of bundling the interior of edges are that ii¾?tangents at endpoints deviate from the line connecting the two endpoints in an uncontrolled way and iii¾?there is ambiguity as to which pairs of vertices are actually connected. Both severely reduce the interpretability of geographic network visualizations. We therefore propose methods that bundle edges at their ends rather than their interior. This way, tangents at vertices point in the general direction of all neighbors of edges in the bundle, and ambiguity is avoided altogether. For undirected graphs our approach yields curves with no more than one turning point. For directed graphs we introduce a new drawing style, confluent spiral drawings, in which the direction of edges can be inferred from monotonically increasing curvature along each spiral segment.

Untangling Hairballs

Small-world graphs have characteristically low average distance and thus cause force-directed methods to generate drawings that look like hairballs. This is by design as the inherent objective of these methods is a globally uniform edge length or, more generally, accurate distance representation. The problem arises in graphs of high density or high conductance, and in the presence of high-degree vertices, all of which tend to pull vertices together and thus clutter variation in local density. We here propose a method to draw online social networks, a special class of hairball graphs. The method is based on a spanning subgraph that is sparse but connected and consists of strong ties holding together communities. To identify these ties we propose a novel measure of embeddedness. It is based on a weighted accumulation of triangles in quadrangles and can be determined efficiently. An evaluation on empirical and generated networks indicates that our approach improves upon previous methods using other edge indices. Although primarily designed to achieve more informative drawings, our spanning subgraph may also serve as a sparsifier that trims a hairball graph before the application of a clustering algorithm.

Adaptive Disentanglement Based on Local Clustering in Small-World Network Visualization

Small-world networks have characteristically low pairwise shortest-path distances, causing distance-based layout methods to generate hairball drawings. Recent approaches thus aim at finding a sparser representation of the graph to amplify variations in pairwise distances. Since the effect of sparsification on the layout is difficult to describe analytically, the incorporated filtering parameters of these approaches typically have to be selected manually and individually for each input instance. We here propose the use of graph invariants to determine suitable parameters automatically. This allows us to perform adaptive filtering to obtain drawings in which the cluster structure is most prominent. The approach is based on an empirical relationship between input and output characteristics that is derived from real and synthetic networks. Experimental evaluation shows the effectiveness of our approach and suggests that it can be used by default to increase the robustness of force-directed layout methods.

Minimum-Displacement Overlap Removal for Geo-referenced Data Visualization

Given a set of rectangles embedded in the plane, we consider the problem of adjusting the layout to remove all overlap while preserving the orthogonal order of the rectangles. The objective is to minimize the displacement of the rectangles. We call this problem Minimum-Displacement Overlap Removal (mdor). Our interest in this problem is motivated by the application of displaying metadata of archaeological sites. Because most existing overlap removal algorithms are not designed to minimize displacement while preserving orthogonal order, we present and compare several approaches which are tailored to our particular usecase. We introduce a new overlap removal heuristic which we call reArrange. Although conceptually simple, it is very effective in removing the overlap while keeping the displacement small. Furthermore, we propose an additional procedure to repair the orthogonal order after every iteration, with which we extend both our new heuristic and PRISM, a widely used overlap removal algorithm. We compare the performance of both approaches with and without this order repair method. The experimental results indicate that reArrange is very effective for heterogeneous input data where the overlap is concentrated in few dense regions.

Node overlap removal by growing a tree

Node overlap removal is a necessary step in many scenarios including laying out a graph, or visualizing a tag cloud. Our contribution is a new overlap removal algorithm that iteratively builds a Minimum Spanning Tree on a Delaunay triangulation of the node centers and removes the node overlaps by “growing” the tree. The algorithm is simple to implement yet produces high quality layouts. According to our experiments it runs several times faster than the current state-of-the-art methods.

Flexible Level-of-Detail Rendering for Large Graphs

Given a set of n rectangles embedded in the Euclidian plane, we consider the problem of modifying the layout to avoid intersections of the rectangles. The objective is to minimize the total displacement under the additional constraint that the orthogonal order of the rectangles must be preserved. We call this problem minimum-displacement overlap removal (mdor). We define the total displacement in the new layout as the sum of the Euclidian distances between the initial position (x, y) and the final position (x′, y′) of the centers of all rectangles. A layout adjustment is orthogonal-order preserving if the order of the rectangles with respect to the xand the y-axis does not change. More formally, the order is preserved if and only if for any pair of rectangles ri and rj it holds that xi ≤ xj ⇒ xi ≤ xj and that yi ≤ yj ⇒ y′ i ≤ y′ j .Computer networks and distributed systems are typically represented as graphs, and sooner or later everybody working in distributed computing is facing a graph drawing problem. In my talk I will discuss a few artifacts in distributed computing that are related to graph theory and graph drawing. The focus of my talk will be wireless communication networks. While a vertex in a wireless network is simply some kind of communication device, vertices are not necessarily connected by edges, but rather “unplugged.” We discuss the following “family of open problems”: How well can we draw a wireless network modeled by a UDG, QUDG, BIG, or UBG, using connectivity, interference, distance, angle, or multipath information, to understand which node is which? Does such a drawing help to design better routing or media access protocols? The Role of Visual Analytics in Exploring Graph DataThis is the arXiv index for the electronic proceedings of the 24th International Symposium on Graph Drawing and Network Visualization (GD 2016), which was held in Athens, Greece, September 19-21 2016. It contains the peer-reviewed and revised accepted papers with an optional appendix.The visualization of graphs using classical node-link diagrams works well up to the point where the number of nodes exceeds the capacity of the display. To overcome this limitation Zinsmaier et al. [5] proposed a rendering technique which aggregates nodes based on their spatial distribution, thereby allowing for visual exploration of large graphs. Since the rendering is done on the graphics processing unit (GPU) this process is reasonably fast. However, the connection between input graph and visual image is partially lost, which makes it harder, for instance, to process weights and labels of the input graph.