Learn More
introduced the notion of a vector coloring of a graph. In particular, they showed that every k-colorable graph is also vector k-colorable, and that for constant k, graphs that are vector k-colorable can be colored by roughly ∆ 1−2/k colors. Here ∆ is the maximum degree in the graph and is assumed to be of the order of n δ for some 0 < δ < 1. Their results(More)
MAX CUT is the problem of partitioning the vertices of a graph into two sets, maximizing the number of edges joining these sets. This problem is NP-hard. Goemans and Williamson proposed an algorithm that first uses a semidefinite programming relaxation of MAX CUT to embed the vertices of the graph on the surface of an <italic>n</italic> dimensional sphere,(More)
—A major open question in communication complexity is if randomized and quantum communication are polynomially related for all total functions. So far, no gap larger than a power of two is known, despite significant efforts. We examine this question in the number-on-the-forehead model of multiparty communication complexity. We show that essentially all(More)
We consider the problem of embedding vectors from an arbitrary Euclidean space into a low dimensional Euclidean space, while preserving up to a small distortion, a subset of the distances. In particular, preserving only the distance of each vector to a small number of its nearest neighbors. We show that even when the subset of distances we wish to preserve(More)