The Impact of Shape on the Perception of Euler Diagrams

Euler diagrams are often used for visualizing data collected into sets. However, there is a significant lack of guidance regarding graphical choices for Euler diagram layout. To address this deficiency, this paper asks the question `does the shape of a closed curve affect a user's comprehension of an Euler diagram?' By empirical study, we establish that curve shape does indeed impact on understandability. Our analysis of performance data indicates that circles perform best, followed by squares, with ellipses and rectangles jointly performing worst. We conclude that, where possible, circles should be used to draw effective Euler diagrams. Further, the ability to discriminate curves from zones and the symmetry of the curve shapes is argued to be important. We utilize perceptual theory to explain these results. As a consequence of this research, improved diagram layout decisions can be made for Euler diagrams whether they are manually or automatically drawn

Visual Similarity Perception of Directed Acyclic Graphs: A Study on Influencing Factors

While visual comparison of directed acyclic graphs (DAGs) is commonly encountered in various disciplines (e.g., finance, biology), knowledge about humans' perception of graph similarity is currently quite limited. By graph similarity perception we mean how humans perceive commonalities and differences in graphs and herewith come to a similarity judgment. As a step toward filling this gap the study reported in this paper strives to identify factors which influence the similarity perception of DAGs. In particular, we conducted a card-sorting study employing a qualitative and quantitative analysis approach to identify 1) groups of DAGs that are perceived as similar by the participants and 2) the reasons behind their choice of groups. Our results suggest that similarity is mainly influenced by the number of levels, the number of nodes on a level, and the overall shape of the graph.Comment: Graph Drawing 2017 - arXiv Version; Keywords: Graphs, Perception, Similarity, Comparison, Visualizatio

Compact Drawings of 1-Planar Graphs with Right-Angle Crossings and Few Bends

We study the following classes of beyond-planar graphs: 1-planar, IC-planar, and NIC-planar graphs. These are the graphs that admit a 1-planar, IC-planar, and NIC-planar drawing, respectively. A drawing of a graph is 1-planar if every edge is crossed at most once. A 1-planar drawing is IC-planar if no two pairs of crossing edges share a vertex. A 1-planar drawing is NIC-planar if no two pairs of crossing edges share two vertices. We study the relations of these beyond-planar graph classes (beyond-planar graphs is a collective term for the primary attempts to generalize the planar graphs) to right-angle crossing (RAC) graphs that admit compact drawings on the grid with few bends. We present four drawing algorithms that preserve the given embeddings. First, we show that every $n$-vertex NIC-planar graph admits a NIC-planar RAC drawing with at most one bend per edge on a grid of size $O(n) \times O(n)$. Then, we show that every $n$-vertex 1-planar graph admits a 1-planar RAC drawing with at most two bends per edge on a grid of size $O(n^3) \times O(n^3)$. Finally, we make two known algorithms embedding-preserving; for drawing 1-planar RAC graphs with at most one bend per edge and for drawing IC-planar RAC graphs straight-line

Environment friendly degradation and detoxification of Congo red dye and textile industry wastewater by a newly isolated Bacillus cohnni (RKS9)

Textile industry wastewater (TIWW) is a major source of environmental pollution causing serious threats to all life forms and thus, it must be adequately treated before its final discharge for the safety of environment and public health. In the present study, a potential bacterial strain (RKS9) was isolated from textile (wastewater & sludge) sample for the effective treatment of TIWW resulting in a significant reduction in pollution parameters such as ADMI color (93.87%), COD (77.35%), BOD (86.02%), TDS (66.75%), TOC (67.25%), TSS (60.34%), and phenol (68.55%) within 48 h. This bacterium also decolorized 99% of Congo red dye (100 mg L−1) within 12 h and removed 59.76%, 40.51%, 52.71% and 26.51% cadmium, chromium, lead and nickel, respectively from the TIWW. The activities of azoreductase, laccase, lignin peroxidase (LiP) and manganese peroxidase (MnP) was monitored and metabolites produced during the treatment of dye and TIWW were also analyzed by FT-IR and GC–MS. The phytotoxicity of the untreated and treated TIWW was assessed by seed germination and seedling growth parameters of Phaseolus mungo L. and results showed a significant reduction in the toxicity of the treated TIWW, suggesting that the isolated bacterium RKS9 has a remarkable potential to effectively decolorize/detoxify TIWW

Convexity-Increasing Morphs of Planar Graphs

We study the problem of convexifying drawings of planar graphs. Given any planar straight-line drawing of an internally 3-connected graph, we show how to morph the drawing to one with strictly convex faces while maintaining planarity at all times. Our morph is convexity-increasing, meaning that once an angle is convex, it remains convex. We give an efficient algorithm that constructs such a morph as a composition of a linear number of steps where each step either moves vertices along horizontal lines or moves vertices along vertical lines. Moreover, we show that a linear number of steps is worst-case optimal. To obtain our result, we use a well-known technique by Hong and Nagamochi for finding redrawings with convex faces while preserving y-coordinates. Using a variant of Tutte's graph drawing algorithm, we obtain a new proof of Hong and Nagamochi's result which comes with a better running time. This is of independent interest, as Hong and Nagamochi's technique serves as a building block in existing morphing algorithms.Comment: Preliminary version in Proc. WG 201

GiViP: A Visual Profiler for Distributed Graph Processing Systems

Analyzing large-scale graphs provides valuable insights in different application scenarios. While many graph processing systems working on top of distributed infrastructures have been proposed to deal with big graphs, the tasks of profiling and debugging their massive computations remain time consuming and error-prone. This paper presents GiViP, a visual profiler for distributed graph processing systems based on a Pregel-like computation model. GiViP captures the huge amount of messages exchanged throughout a computation and provides an interactive user interface for the visual analysis of the collected data. We show how to take advantage of GiViP to detect anomalies related to the computation and to the infrastructure, such as slow computing units and anomalous message patterns.Comment: Appears in the Proceedings of the 25th International Symposium on Graph Drawing and Network Visualization (GD 2017

On the Recognition of Fan-Planar and Maximal Outer-Fan-Planar Graphs

Fan-planar graphs were recently introduced as a generalization of 1-planar graphs. A graph is fan-planar if it can be embedded in the plane, such that each edge that is crossed more than once, is crossed by a bundle of two or more edges incident to a common vertex. A graph is outer-fan-planar if it has a fan-planar embedding in which every vertex is on the outer face. If, in addition, the insertion of an edge destroys its outer-fan-planarity, then it is maximal outer-fan-planar. In this paper, we present a polynomial-time algorithm to test whether a given graph is maximal outer-fan-planar. The algorithm can also be employed to produce an outer-fan-planar embedding, if one exists. On the negative side, we show that testing fan-planarity of a graph is NP-hard, for the case where the rotation system (i.e., the cyclic order of the edges around each vertex) is given

The Marketing Firm: Retailer and consumer contingencies

acceptedVersionpublishedVersio

Exploring the effects of colouring graph diagrams on people of various backgrounds

Colour is one of the primary aesthetic elements of a visualization. It is often used successfully to encode information such as the importance of a particular part of the diagram or the relationship between two parts. Even so, there are few investigations into the human reading of colour coding on diagrams from the scientific community. In this paper we report on an experiment with graph diagrams comparing a black and white composition with two other colour treatments. We drew our subjects from engineering, art, visual design, physical education, tourism, psychology and social science disciplines. We found that colouring the nodes of interest reduced the time taken to find the shortest path between the two nodes for all subjects. Engineers, tourism and social scientists proved significantly faster with artist/designers just below the overall average speed. From this study, we contribute that adding particular colour treatments to diagrams increases legibility. In addition, preliminary work investigating colour treatments and schemes indicates potential for future gains. © 2014 Springer-Verlag