We study the topological simplification of graphs via random embeddings, leading ultimately to a reduction of the Gupta-Newman-Rabinovich-Sinclair (GNRS) L1 embedding conjecture t...
Consider the edge-connectivity survivable network design problem: given a graph G = (V, E) with edge-costs, and edgeconnectivity requirements rij Z0 for every pair of vertices i,...
We describe the first algorithm to compute maximum flows in surface-embedded graphs in near-linear time. Specifically, given a graph embedded on a surface of genus g, with two spe...
Non-relativization of complexity issues can be interpreted as giving some evidence that these issues cannot be resolved by "black-box" techniques. In the early 1990'...
Russell Impagliazzo, Valentine Kabanets, Antonina ...
Let K be a polytope in Rn defined by m linear inequalities. We give a new Markov Chain algorithm to draw a nearly uniform sample from K. The underlying Markov Chain is the first t...