Narrow Results

A t-spanner of a network is a subnetwork in which every two nodes that were connected by an edge in the original network are connected by a path of at most t edges in the subnetwork. This guarantees that if nodes u and v are at distance d(u,v) in the original network, they are at distance no more than t·d(u,v) in the t-spanner. We introduce a more general definition of spanners. A special case of this more general definition is the additive t-spanner: a subnetwork in which every two nodes u and v that were separated by distance d(u,v) in the original network are at distance no more than t+d(u,v) in the subnetwork. We construct low-degree additive t-spanners for hypercubes.