Timeslices are often used to draw and visualize dynamic graphs. While timeslices are a natural way to think about dynamic graphs, they are routinely imposed on continuous data. Often, it is unclear how many timeslices to select: too few timeslices can miss temporal features such as causality or even graph structure while too many timeslices slows the drawing computation. We present a model for dynamic graphs which is not based on timeslices, and a dynamic graph drawing algorithm, DynNoSlice, to draw graphs in this model. In our evaluation, we demonstrate the advantages of this approach over timeslicing on continuous data sets.
Offline Drawing. Offline dynamic graph drawing algorithms capture all of the dynamic data beforehand and optimize across it simultaneously. Foresighted layout algorithms @cite_34 @cite_16 are among the first attempts at offline dynamic graph drawing. They create a supergraph as the union of the elements at each timeslice. The supergraph is then used to define the position of nodes and edge bends. Mental map preservation is the primary focus of this approach.
@cite_34 @cite_16
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In this paper we present a generic algorithm for drawing sequences of graphs. This algorithm works for different layout algorithms and related metrics and adjustment strategies. It differs from previous work on dynamic graph drawing in that it considers all graphs in the sequence (offline) instead of just the previous ones (online) when computing the layout for each graph of the sequence. We introduce several general adjustment strategies and give examples of these strategies in the context of force-directed graph layout. Finally some results from our first prototype implementation are discussed. In this paper we present a generic algorithm for drawing sequences of graphs. This algorithm works for different layout algorithms and related metrics and adjustment strategies. It differs from previous work on dynamic graph drawing in that it considers all graphs in the sequence (offline) instead of just the previous ones (online) when computing the layout for each graph of the sequence. We introduce several general adjustment strategies and give examples of these strategies in the context of force-directed graph layout. Finally some results from our first prototype implementation are discussed. We initiate the study of graph sketching, i.e., algorithms that use a limited number of linear measurements of a graph to determine the properties of the graph. While a graph on n nodes is essentially O(n2)-dimensional, we show the existence of a distribution over random projections into d-dimensional "sketch" space (d<< n2) such that the relevant properties of the original graph can be inferred from the sketch with high probability. Specifically, we show that: 1. d = O(n · polylog n) suffices to evaluate properties including connectivity, k-connectivity, bipartiteness, and to return any constant approximation of the weight of the minimum spanning tree. 2. d = O(n1+γ) suffices to compute graph sparsifiers, the exact MST, and approximate the maximum weighted matchings if we permit O(1 γ)-round adaptive sketches, i.e., a sequence of projections where each projection may be chosen dependent on the outcome of earlier sketches. Our results have two main applications, both of which have the potential to give rise to fruitful lines of further research. First, our results can be thought of as giving the first compressed-sensing style algorithms for graph data. Secondly, our work initiates the study of dynamic graph streams. There is already extensive literature on processing massive graphs in the data-stream model. However, the existing work focuses on graphs defined by a sequence of inserted edges and does not consider edge deletions. We think this is a curious omission given the existing work on both dynamic graphs in the non-streaming setting and dynamic geometric streaming. Our results include the first dynamic graph semi-streaming algorithms for connectivity, spanning trees, sparsification, and matching problems. In dynamic graph drawing, the input is a sequence of graphs for which a sequence of layouts is to be generated such that the quality of individual layouts is balanced with layout stability over time. Qualitatively different extensions of drawing algorithms for static graphs to the dynamic case have been proposed, but little is known about their relative utility. We report on a quantitative study comparing the three prototypical extensions via their adaptation for the stress-minimization framework. While some findings are more subtle, the linking approach connecting consecutive instances of the same vertex is found to be the overall method of choice.