Graph reordering is a powerful technique to increase the locality of the representations of graphs, which can be helpful in several applications. We study how the technique can be used to improve compression of graphs and inverted indexes. We extend the recent theoretical model of Chierichetti et al. (KDD 2009) for graph compression, and show how it can be employed for compression-friendly reordering of social networks and web graphs and for assigning document identifiers in inverted indexes. We design and implement a novel theoretically sound reordering algorithm that is based on recursive graph bisection. Our experiments show a significant improvement of the compression rate of graph and indexes over existing heuristics. The new method is relatively simple and allows efficient parallel and distributed implementations, which is demonstrated on graphs with billions of vertices and hundreds of billions of edges
We show how to improve the Sugiyama scheme by edge bundling. Our method modifies the layout produced by the Sugiyama scheme by bundling some of the edges together. The bundles are created by a new algorithm based on minimizing the total ink needed to draw the graph edges. We give several implementations that vary in quality of the resulting layout and execution time. To diminish the number of edge crossings inside of the bundles we apply a metroline crossing minimization technique. The method preserves the Sugiyama style of the layout and creates a more readable view of the graph.
A queue layout of a graph G consists of a linear order of the vertices of G and a partition of the edges of G into queues, so that no two independent edges of the same queue are nested. The queue number of G is the minimum number of queues required by any queue layout of G.In this paper, we continue the study of the queue number of planar 3trees. As opposed to general planar graphs, whose queue number is not known to be bounded by a constant, the queue number of planar 3-trees has been shown to be at most seven. In this work, we improve the upper bound to five. We also show that there exist planar 3-trees, whose queue number is at least four; this is the first example of a planar graph with queue number greater than three.
Abstract. We propose a new approach to edge bundling. At the first stage we route the edge paths so as to minimize a weighted sum of the total length of the paths together with their ink. As this problem is NP-hard, we provide an efficient heuristic that finds an approximate solution. The second stage then separates edges belonging to the same bundle. To achieve this, we provide a new and efficient algorithm that solves a variant of the metro-line crossing minimization problem. The method creates aesthetically pleasing edge routes that give an overview of the global graph structure, while still drawing each edge separately, without intersecting graph nodes, and with few crossings.
Abstract. We study the problem of computing semantics-preserving word clouds in which semantically related words are close to each other. We implement three earlier algorithms for creating word clouds and three new ones. We define several metrics for quantitative evaluation of the resulting layouts. Then the algorithms are compared according to these metrics, using two data sets of documents from Wikipedia and research papers. We show that two of our new algorithms outperform all the others by placing many more pairs of related words so that their bounding boxes are adjacent. Moreover, this improvement is not achieved at the expense of significantly worsened measurements for the other metrics.
Abstract. Reducing the number of edge crossings is considered one of the most important graph drawing aesthetics. While real-world graphs tend to be large and dense, most of the earlier work on evaluating the impact of edge crossings utilizes relatively small graphs that are manually generated and manipulated. We study the effect on task performance of increased edge crossings in automatically generated layouts for graphs, from different datasets, with different sizes, and with different densities. The results indicate that increasing the number of crossings negatively impacts accuracy and performance time and that impact is significant for small graphs but not significant for large graphs. We also quantitatively evaluate the impact of edge crossings on crossing angles and stress in automatically constructed graph layouts. We find a moderate correlation between minimizing stress and the minimizing the number of crossings.
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