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...
Let H be a graph, and let CH(G) be the number of (subgraph isomorphic) copies of H contained in a graph G. We investigate the fundamental problem of estimating CH(G). Previous res...
We introduce a hierarchical partitioning scheme of the Euclidean plane, called circular partitions. Such a partition consists of a hierarchy of convex polygons, each having small ...
We show that the problem of computing a minimum distortion embedding of a given graph into a path remains NP-hard when the input graph is restricted to a bipartite, cobipartite, o...
We present the first constant-factor approximation algorithm for network design with multiple commodities and economies of scale. We consider the rent-or-buy problem, a type of m...