GPU-Based Parallel Particle Swarm Optimization Methods for Graph Drawing

Particle Swarm Optimization (PSO) is a population-based stochastic search technique for solving optimization problems, which has been proven to be effective in a wide range of applications. However, the computational efficiency on large-scale problems is still unsatisfactory. A graph drawing is a pictorial representation of the vertices and edges of a graph. Two PSO heuristic procedures, one serial and the other parallel, are developed for undirected graph drawing. Each particle corresponds to a different layout of the graph. The particle fitness is defined based on the concept of the energy in the force-directed method. The serial PSO procedure is executed on a CPU and the parallel PSO procedure is executed on a GPU. Two PSO procedures have different data structures and strategies. The performance of the proposed methods is evaluated through several different graphs. The experimental results show that the two PSO procedures are both as effective as the force-directed method, and the parallel procedure is more advantageous than the serial procedure for larger graphs

Elastic-based multi-scale graph drawing

Graph drawing is an important information visualization technique with applications in a variety of disciplines, including VLSI design, bioinformatics, geography, and social network analysis. We present a new force-directed, multi-scale algorithm for the drawing of undirected graphs, using the analogy of elastics (with an unstretched length of zero), instead of springs, resulting in a force model similar to that of Tutte[65] that produces competitive results on a variety of problems

A Distributed Multilevel Force-directed Algorithm

The wide availability of powerful and inexpensive cloud computing services naturally motivates the study of distributed graph layout algorithms, able to scale to very large graphs. Nowadays, to process Big Data, companies are increasingly relying on PaaS infrastructures rather than buying and maintaining complex and expensive hardware. So far, only a few examples of basic force-directed algorithms that work in a distributed environment have been described. Instead, the design of a distributed multilevel force-directed algorithm is a much more challenging task, not yet addressed. We present the first multilevel force-directed algorithm based on a distributed vertex-centric paradigm, and its implementation on Giraph, a popular platform for distributed graph algorithms. Experiments show the effectiveness and the scalability of the approach. Using an inexpensive cloud computing service of Amazon, we draw graphs with ten million edges in about 60 minutes.Comment: Appears in the Proceedings of the 24th International Symposium on Graph Drawing and Network Visualization (GD 2016

Representing Space: A Hybrid Genetic Algorithm for Aesthetic Graph Layout

This paper describes a hybrid Genetic Algorithm (GA) that is used to improve the layout of a graph according to a number of aesthetic criteria. The GA incorporates spatial and topological information by operating directly with a graph based representation. Initial results show this to be a promising technique for positioning graph nodes on a surface and may form the basis of a more general approach for problems involving multi-criteria spatial optimisation

Node-attribute graph layout for small-world networks

Small-world networks are a very commonly occurring type of graph in the real-world, which exhibit a clustered structure that is not well represented by current graph layout algorithms. In many cases we also have information about the nodes in such graphs, which are typically depicted on the graph as node colour, shape or size. Here we demonstrate that these attributes can instead be used to layout the graph in high-dimensional data space. Then using a dimension reduction technique, targeted projection pursuit, the graph layout can be optimised for displaying clustering. The technique out-performs force-directed layout methods in cluster separation when applied to a sample, artificially generated, small-world network

Persistent Homology Guided Force-Directed Graph Layouts

Graphs are commonly used to encode relationships among entities, yet their abstractness makes them difficult to analyze. Node-link diagrams are popular for drawing graphs, and force-directed layouts provide a flexible method for node arrangements that use local relationships in an attempt to reveal the global shape of the graph. However, clutter and overlap of unrelated structures can lead to confusing graph visualizations. This paper leverages the persistent homology features of an undirected graph as derived information for interactive manipulation of force-directed layouts. We first discuss how to efficiently extract 0-dimensional persistent homology features from both weighted and unweighted undirected graphs. We then introduce the interactive persistence barcode used to manipulate the force-directed graph layout. In particular, the user adds and removes contracting and repulsing forces generated by the persistent homology features, eventually selecting the set of persistent homology features that most improve the layout. Finally, we demonstrate the utility of our approach across a variety of synthetic and real datasets