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We consider the variation of Ramsey numbers introduced by Erdos and Pach [J. Graph Theory, 7 (1983), pp. 137-147], where instead of seeking complete or independent sets we only seek a t-homogeneous set, a vertex subset that induces a subgraph of minimum de ...
Real-life acquisition systems are fundamentally limited in their ability to reproduce point sources. For example, a point source object, a star say, observed with an optical telescope is blurred by the imperfect lenses composing the system. Mathematically, ...
Over the past few decades we have been experiencing an explosion of information generated by large networks of sensors and other data sources. Much of this data is intrinsically structured, such as traffic evolution in a transportation network, temperature ...
Weighted undirected graphs are a simple, yet powerful way to encode structure in data. A first question we need to address regarding such graphs is how to use them effectively to enhance machine learning problems. A second but more important question is ho ...
The standard LP relaxation of the asymmetric traveling salesman problem has been conjectured to have a constant integrality gap in the metric case. We prove this conjecture when restricted to shortest path metrics of node-weighted digraphs. Our arguments a ...
We give a constant factor approximation algorithm for the Asymmetric Traveling Salesman Problem on shortest path metrics of directed graphs with two different edge weights. For the case of unit edge weights, the first constant factor approximation was give ...
We study the problem of matrix completion when infor- mation about row or column proximities is available, in the form of weighted graphs. The problem can be formulated as the optimization of a convex function that can be solved efficiently using the alter ...
We consider the problem of designing spectral graph filters for the construction of dictionaries of atoms that can be used to efficiently represent signals residing on weighted graphs. While the filters used in previous spectral graph wavelet constructions ...
Institute of Electrical and Electronics Engineers2015
A diameter graph in is a graph whose set of vertices is a finite subset of and whose set of edges is formed by pairs of vertices that are at diameter apart. This paper is devoted to the study of different extremal properties of diameter graphs in and on a ...
A faithful (unit) distance graph in R-d is a graph whose set of vertices is a finite subset of the d-dimensional Euclidean space, where two vertices are adjacent if and only if the Euclidean distance between them is exactly 1. A (unit) distance graph in Rd ...
