Edge Routing with Ordered Bundles

Edge bundling reduces the visual clutter in a drawing of a graph by uniting the edges into bundles. We propose a method of edge bundling drawing each edge of a bundle separately as in metro-maps and call our method ordered bundles. To produce aesthetically looking edge routes it minimizes a cost function on the edges. The cost function depends on the ink, required to draw the edges, the edge lengths, widths and separations. The cost also penalizes for too many edges passing through narrow channels by using the constrained Delaunay triangulation. The method avoids unnecessary edge-node and edge-edge crossings. To draw edges with the minimal number of crossings and separately within the same bundle we develop an efficient algorithm solving a variant of the metro-line crossing minimization problem. In general, the method creates clear and smooth edge routes giving an overview of the global graph structure, while still drawing each edge separately and thus enabling local analysis

Evaluating Visual Realism in Drawing Areas of Interest on UML Diagrams

Areas of interest (AOIs) are defined as an addition to UML diagrams: groups of elements of system architecture diagrams that share some common property. Some methods have been proposed to automatically draw AOIs on UML diagrams. However, it is not clear how users perceive the results of such methods as compared to human-drawn areas of interest. We present here a process of studying and improving the perceived quality of computer-drawn AOIs. We qualitatively evaluated how users perceive the quality of computer- and human-drawn AOIs, and used these results to improve an existing algorithm for drawing AOIs. Finally, we designed a quantitative comparison for AOI drawings and used it to show that our improved renderings are closer to human drawings than the original rendering algorithm results. The combined user evaluation, algorithmic improvements, and quantitative comparison support our claim of improving the perceived quality of AOIs rendered on UML diagrams.

A Coloring Algorithm for Disambiguating Graph and Map Drawings

Drawings of non-planar graphs always result in edge crossings. When there are many edges crossing at small angles, it is often difficult to follow these edges, because of the multiple visual paths resulted from the crossings that slow down eye movements. In this paper we propose an algorithm that disambiguates the edges with automatic selection of distinctive colors. Our proposed algorithm computes a near optimal color assignment of a dual collision graph, using a novel branch-and-bound procedure applied to a space decomposition of the color gamut. We give examples demonstrating the effectiveness of this approach in clarifying drawings of real world graphs and maps

The logic engine and the realization problem for nearest neighbor graphs

AbstractRoughly speaking, a “nearest neighbor graph” is formed from a set of points in the plane by joining two points if one is the nearest neighbor of the other. There are several ways in which this intuitive concept can be made precise.This paper investigates the complexity of determining whether, for a given graph G, there is a set of points P in the plane such that G is isomorphic to a nearest neighbor graph on P. We show that this problem is NP-hard for several definitions of nearest neighbor graph.Our proof technique uses an interesting simulation of a mechanical device called a “logic engine”

String graphs and separators

String graphs, that is, intersection graphs of curves in the plane, have been studied since the 1960s. We provide an expository presentation of several results, including very recent ones: some string graphs require an exponential number of crossings in every string representation; exponential number is always sufficient; string graphs have small separators; and the current best bound on the crossing number of a graph in terms of the pair-crossing number. For the existence of small separators, unwrapping the complete proof include generally useful results on approximate flow-cut dualities.Comment: Expository paper based on course note

Edge routing with ordered bundles

Edge bundling reduces the visual clutter in a drawing of a graph by uniting the edges into bundles. We propose a method of edge bundling that draws each edge of a bundle separately as in metro-maps and call our method ordered bundles. To produce aesthetically looking edge routes, it minimizes a cost function on the edges. The cost function depends on the ink, required to draw the edges, the edge lengths, widths and separations. The cost also penalizes for too many edges passing through narrow channels by using the constrained Delaunay triangulation. The method avoids unnecessary edge-node and edge-edge crossings. To draw edges with the minimal number of crossings and separately within the same bundle, we develop an efficient algorithm solving a variant of the metro-line crossing minimization problem. In general, the method creates clear and smooth edge routes giving an overview of the global graph structure, while still drawing each edge separately and thus enabling local analysis. © 2015 Elsevier B.V