Distance oracles and graph spanners are excerpts of a graph that allow to compute approximate shortest paths. Here, we consider the situation where it is possible to access the ori...
Let S be the boundary of a convex polytope of dimension d + 1, or more generally let S be a convex polyhedral pseudomanifold. We prove that S has a polyhedral nonoverlapping unfold...
We initiate an investigation of sublinear algorithms for geometric problems in two and three dimensions. We give optimal algorithms for intersection detection of convex polygons a...
A ball graph is an intersection graph of a set of balls with arbitrary radii. Given a real number t > 1, we say that a subgraph G′ of a graph G is a t-spanner of G, if for eve...
A core-based group-shared multicast tree is a shortest path tree rooted at core node that distributes packets to and from all group members. Traditionally, the bandwidth cost cons...