Graph layout algorithms are used to compute aesthetic and useful visualizations of graphs. In general, for graphs with up to a few hundred nodes, force-directed layout algorithms produce good layouts. Unfortunately, for larger graphs, they often get stuck at local minima and have high computational complexity. In this paper, we introduce a novel message passing technique for graph layout. The k...

We focus on the problem of estimating the graph structure associated with a discrete Markov random field. We describe a method based on `1regularized logistic regression, in which the neighborhood of any given node is estimated by performing logistic regression subject to an `1-constraint. Our framework applies to the high-dimensional setting, in which both the number of nodes p and maximum nei...

As a general framework to determine a collision-free feedback motion strategies, the Random Neighborhood Graph (RNG) approach [19] defines a global navigation function over an approximate representation of the free configuration. In this paper, we improve the RNG approach in several aspects. We present an ANN-accelerated RNG construction algorithm to achieve near logarithmic running time in eac...

Let G be a graph, u be a vertex of G, and B(u)(or BG(u)) be the set of u with all its neighbors in G. A sequence (B1, B2, ..., Bn) of subsets of an n-set S is a neighborhood sequence if there exists a graph G with a vertex set S and a permutation (v1, v2, ..., vn) of S such that B(vi) = Bi for i = 1, 2, ..., n. Define Aut(B1, B2, ..., Bn) as the set {f : f is a permutation of V (G) and (f(B1), ...

Visualization of high-dimensional data, such as text documents, is useful to map out the similarities among various data points. In the high-dimensional space, documents are commonly represented as bags of words, with dimensionality equal to the vocabulary size. Classical approaches to document visualization directly reduce this into visualizable two or three dimensions. Recent approaches consi...

Descent methods for combinatorial optimization proceed by performing a sequence of local changes on an initial solution which improve each time the value of an objective function until a local optimum is found. Several metaheuristics have been proposed which extend in various ways this scheme and avoid being trapped in local optima. For example, Hansen and Mladenovic have recently proposed the ...