Drawing Large Graphs by Multilevel Maxent-Stress Optimization

Drawing Large Graphs by Low-Rank Stress Majorization

Optimizing a stress model is a natural technique for drawing graphs: one seeks an embedding into Rd which best preserves the induced graph metric. Current approaches to solving the stress model for a graph with |V| nodes and |E| edges require the full all-pairs shortest paths (APSP) matrix, which takes O(|V|2 log |E|+ |V||E|) time and O(|V|2) space. We propose a novel algorithm based on a low-r...

Drawing Large Graphs with a Potential-Field-Based Multilevel Algorithm

Force-directed graph drawing algorithms are widely used for drawing general graphs. However, these methods do not guarantee a sub-quadratic running time in general. We present a new force-directed method that is based on a combination of an efficient multilevel scheme and a strategy for approximating the repulsive forces in the system by rapidly evaluating potential fields. Given a graph G = (V...

Drawing Huge Graphs by Algebraic Multigrid Optimization

We present an extremely fast graph drawing algorithm for very large graphs, which we term ACE (for Algebraic multigrid Computation of Eigenvectors). ACE exhibits a vast improvement over the fastest algorithms we are currently aware of; using a serial PC, it draws graphs of millions of nodes in less than a minute. ACE finds an optimal drawing by minimizing a quadratic energy function. The minimi...

Drawing Dynamic Graphs by Stress Minimization

Maxent-Stress Optimization of 3D Biomolecular Models

Knowing a biomolecule’s structure is inherently linked to and a prerequisite for any detailed understanding of its function. Significant effort has gone into developing technologies for structural characterization. These technologies do not directly provide 3D structures; instead they typically yield noisy and erroneous distance information between specific entities such as atoms or residues, w...