Sublinear-time Algorithms for Stress Minimization in Graph Drawing

Abstract

We present algorithms reducing the runtime of the stress minimization iteration of stress-based layouts to sublinear in the number of vertices and edges. Specifically, we use vertex sampling to further reduce the number of vertex pairs considered in stress minimization iterations. Moreover, we use spectral sparsification to reduce the number of edges considered in stress minimization computations to sublinear in the number of edges, esp. for dense graphs.Specifically, we present new pivot selection methods using importance-based sampling. Then, we present two variations of sublinear-time stress minimization method on two popular stress-based layouts, Stress Majorization and Stochastic Gradient Descent.Experimental results demonstrate that our sublinear-time algorithms run, on average, about 35% faster than the state-of-art linear-time algorithms, while obtaining similar quality drawings based on stress and shape-based metrics.