Parameterized algorithms are a very useful tool for dealing with NP-hard problems on graphs. Yet, to properly utilize parameterized algorithms it is necessary to choose the right parameter based on the type of problem and properties of the target graph class. Tree-width is an example of a very successful graph parameter, however it cannot be used on dense graph classes and there also exist prob...

Let G = (V,E) be a graph. A k-neighborhood in G is a set of vertices consisting of all the vertices at distance at most k from some vertex of G. The hypergraph on vertex set V which edge set consists of all the k-neighborhoods of G for all k is the neighborhood hypergraph of G. Our goal in this paper is to investigate the complexity of a graph in terms of its neighborhoods. Precisely, we define...

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...

Local search algorithms exploit moves on an adjacency graph of the search space. An “elementary landscape” exists if the objective function f is an eigenfunction of the Laplacian of the graph induced by the neighborhood operator; this allows various statistics about the neighborhood to be computed in closed form. A new component based model makes it relatively simple to prove that certain types...

We study clustering algorithms based on neighborhood graphs on a random sample of data points. The question we ask is how such a graph should be constructed in order to obtain optimal clustering results. Which type of neighborhood graph should one choose, mutual k-nearest neighbor or symmetric k-nearest neighbor? What is the optimal parameter k? In our setting, clusters are defined as connected...

A permutation graph is an intersection graph of segments lying between two parallel lines. A Seidel complementation of a finite graph at a vertex v consists in complementing the edges between the neighborhood and the non-neighborhood of v. Two graphs are Seidel complement equivalent if one can be obtained from the other by a sequence of Seidel complementations. In this paper we introduce the ne...

Neighborhood-perfect graphs form a subclass of the perfect graphs if the Strong Perfect Graph Conjecture of C. Berge is true. However, they are still not shown to be perfect. Here we propose the characterization of neighborhood-perfect graphs by studying minimal non-neighborhood-perfect graphs (MNNPG). After presenting some properties of MNNPGs, w e show that the only MNNPGs with neighborhood i...