We present a general framework for constructing cut sparsifiers in undirected graphs --- weighted subgraphs for which every cut has the same weight as the original graph, up to a multiplicative… (More)

2008 49th Annual IEEE Symposium on Foundations of…

2008

Given a complete undirected graph, a cost function on edges and a degree bound B, the degree bounded network design problem is to find a minimum cost simple subgraph with maximum degree B satisfying… (More)

Graphs with bounded highway dimension were introduced in [Abraham et al., SODA 2010] as a model of transportation networks. We show that any such graph can be embedded into a distribution over… (More)

We present new approaches to constructing graph sparsifiers — weighted subgraphs for which every cut has the same value as the original graph, up to a factor of (1 ± ǫ). Our first approach… (More)

Bends, T-intersections, U-shape turns and cross-junctions are some variations that can be found frequently in long enclosed spaces. For a receiver located around the bend in the "T" intersection, the… (More)

Citizens travelling between cities and towns rely heavily on a mass transport system in many developed countries. In recent years, many more of these underground railway systems are constructed and… (More)