A Potential-Field-Based Multilevel Algorithm for Drawing Large Graphs

The aim of automatic graph drawing is to compute a well-readable layout of a given graph G=(V,E). One very popular class of algorithms for drawing general graphs are force-directed methods. These methods generate drawings of G in the plane so that each edge is represented by a straight line connecting its two adjacent nodes. The computation of the drawings is based on associating G with a physical model. Then, the algorithms iteratively try to find a placement of the nodes so that the total energy of the physical system is minimal. Several force-directed methods can visualize large graphs containing many thousands of vertices in reasonable time. However, only some of these methods guarantee a sub-quadratic running time in special cases or under certain assumptions, but not in general. The others are not sub-quadratic at all. We develop a new force-directed algorithm that is based on a combination of an efficient multilevel strategy and a method for approximating the repulsive forces in the system by rapidly evaluating potential fields. The worst-case running time of the new method is O(|V| log|V|+|E|) with linear memory requirements. In practice, the algorithm generates nice drawings of graphs containing up to 100000 nodes in less than five minutes. Furthermore, it clearly visualizes even the structures of those graphs that turned out to be challenging for other tested methods

Dessin de graphe assisté par un algorithme génétique

National audienceInteractive visualization interfaces for graph are an interesting perspective for data analysis, and by extension for decision support system. The aim of this project is to assist user for drawing graphs. Currently, one of the main difficulties for the user is to choose the best fitted algorithm for his graph. Indeed, there are lots of different algorithms and few of them are easy to use. The suggested solution is to generate different correct drawings for the same graph. Those drawings are generated by a modified force-directed placement algorithm for which parameters are set vertex by vertex. Parameters set are given by a genetic algorithm. English version : Interactive visualization interfaces for graph are an interesting perspective for data analysis, and by extension for decision support system. The aim of this project is to assist user in drawing graphs. Currently, one of the main difficulties for the user is to choose the best fitted algorithm for his graph. Indeed, there are lots of different algorithms and few of them are easy to use. The suggested solution is to generate different correct drawings for the same graph. Those drawings are generated by a modified force-directed placement algorithm for which parameters are set vertex by vertex. Parameter sets are given by a genetic algorithm. This article presents a proof of concept that this modified algorithm and the associated genetic algorithm are able to reproduce highly constrained drawing (parallel edges or right-angled) in a very different way that what force directed placement algorithms do. The different highlighted points in this article are the mass-spring system and its modification, the genetic algorithm, the similarity method used to evaluate drawing and the proof of concept of the method.Les interfaces de visualisation interactive de graphes représentent aujourd'hui une perspective intéressante pour l'analyse de données, et par extension pour les systèmes d'aide à la décision. Le but de ce projet est d'assister un utilisateur novice dans le cadre du dessin de graphe. Actuellement, une des principales difficultés pour l'utilisateur consiste à choisir l'algorithme de dessin qui conviendra le mieux à son graphe. En effet, il existe un très grand nombre de méthodes possibles et toutes ne sont pas facilement accessibles. La solution envisagée consiste à fournir automatiquement plusieurs dessins viables d'un même graphe. Ces dessins sont générés par un algorithme par modèle de force (système masse-ressort) modifié afin d'être paramétrable sommet par sommet. Les jeux de paramètres sont fournis par un algorithme génétique. Cet article présente principalement une preuve de concept de la possibilité d'utiliser un tel processus pour dessiner tout type de graphe, et plus particulièrement des graphes fortement contraints (angles droits ou parallélismes). Les points abordés sont le modèle masse-ressort utilisé et les modifications qui lui ont été apportées, les caractéristiques principales de l'algorithme génétique mis en œuvre, la métrique de similarité permettant l'évaluation des dessins générés au cours de l'apprentissage et enfin le cas d'application proposé comme preuve de concept

FieldPlacer - A flexible, fast and unconstrained force-directed placement method for heterogeneous reconfigurable logic architectures

The field of placement methods for components of integrated circuits, especially in the domain of reconfigurable chip architectures, is mainly dominated by a handful of concepts. While some of these are easy to apply but difficult to adapt to new situations, others are more flexible but rather complex to realize. This work presents the FieldPlacer framework, a flexible, fast and unconstrained force-directed placement method for heterogeneous reconfigurable logic architectures, in particular for the ever important heterogeneous FPGAs. In contrast to many other force-directed placers, this approach is called ‘unconstrained’ as it does not require a priori fixed logic elements in order to calculate a force equilibrium as the solution to a system of equations. Instead, it is based on a free spring embedder simulation of a graph representation which includes all logic block types of a design simultaneously. The FieldPlacer framework offers a huge amount of flexibility in applying different distance norms (e. g., the Manhattan distance) for the force-directed layout and aims at creating adapted layouts for various objective functions, e. g., highest performance or improved routability. Depending on the individual situation, a runtime-quality trade-off can be considered to either produce a decent placement in a very short time or to generate an exceptionally good placement, which takes longer. An extensive comparison with the latest simulated annealing placement method from the well-known Versatile Place and Route (VPR) framework shows that the FieldPlacer approach can create placements of comparable quality much faster than VPR or, alternatively, generate better placements in the same time. The flexibility in defining arbitrary objective functions and the intuitive adaptability of the method, which, among others, includes different concepts from the field of graph drawing, should facilitate further developments with this framework, e. g., for new upcoming optimization targets like the energy consumption of an implemented design

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

A Potential-Field-Based Multilevel Algorithm for Drawing Large Graphs

The aim of automatic graph drawing is to compute a well-readable layout of a given graph G=(V,E). One very popular class of algorithms for drawing general graphs are force-directed methods. These methods generate drawings of G in the plane so that each edge is represented by a straight line connecting its two adjacent nodes. The computation of the drawings is based on associating G with a physical model. Then, the algorithms iteratively try to find a placement of the nodes so that the total energy of the physical system is minimal. Several force-directed methods can visualize large graphs containing many thousands of vertices in reasonable time. However, only some of these methods guarantee a sub-quadratic running time in special cases or under certain assumptions, but not in general. The others are not sub-quadratic at all. We develop a new force-directed algorithm that is based on a combination of an efficient multilevel strategy and a method for approximating the repulsive forces in the system by rapidly evaluating potential fields. The worst-case running time of the new method is O(|V| log|V|+|E|) with linear memory requirements. In practice, the algorithm generates nice drawings of graphs containing up to 100000 nodes in less than five minutes. Furthermore, it clearly visualizes even the structures of those graphs that turned out to be challenging for other tested methods