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In most cases authors are permitted to post their version of the article (e.g. in Word or Tex form) to their personal website or institutional repository. Authors requiring further information regarding Elsevier's archiving and manuscript policies are encouraged to visit: a b s t r a c t Given a matrix A ∈ R m×n (n vectors in m dimensions), we consider the(More)
Given a real matrix A ∈ R m×n of rank r, and an integer k < r, the sum of the outer products of top k singular vectors scaled by the corresponding singular values provide the best rank-k approximation A k to A. When the columns of A have specific meaning, it might be desirable to find good approximations to A k which use a small number of columns of A. This(More)
We introduce a new force-directed model for computing graph layout. The model bridges the two more popular force directed approaches – the stress and the electrical-spring models – through the binary stress cost function, which is a carefully defined energy function with low descriptive complexity allowing fast computation via a Barnes-Hut scheme. This(More)
We present an algorithm for the layout of undirected compound graphs, relaxing restrictions of previously known algorithms in regards to topology and geometry. The algorithm is based on the traditional force-directed layout scheme with extensions to handle multi-level nesting, edges between nodes of arbitrary nesting levels, varying node sizes, and other(More)
Given a matrix A∈ℝ m×n (n vectors in m dimensions), and a positive integer k<n, we consider the problem of selecting k column vectors from A such that the volume of the parallelepiped they define is maximum over all possible choices. We prove that there exists δ<1 and c>0 such that this problem is not approximable within 2−ck for k=δn, unless P=NP.
We present a fast spectral graph drawing algorithm for drawing undi-rected connected graphs. Classical Multi-Dimensional Scaling yields a quadratic-time spectral algorithm, which approximates the real distances of the nodes in the final drawing with their graph theoretical distances. We build from this idea to develop the linear-time spectral graph drawing(More)