Let S be a set of n points in IRd and let t > 1 be a real number. A t-spanner for S is a graph having the points of S as its vertices such that for any pair p, q of points ther...
We introduce a family of directed geometric graphs, denoted Gθ λ, that depend on two parameters λ and θ. For 0 ≤ θ < π 2 and 1 2 < λ < 1, the Gθ λ graph is a s...
We propose a novel localized algorithm that constructs a bounded degree and planar spanner for wireless ad hoc networks modeled by unit disk graph (UDG). Every node only has to kn...
We give the first polynomial-time approximation scheme (PTAS) for the Steiner forest problem on planar graphs and, more generally, on graphs of bounded genus. As a first step, w...
We present an O( √ n log n)-approximation algorithm for the problem of finding the sparsest spanner of a given directed graph G on n vertices. A spanner of a graph is a sparse ...
Piotr Berman, Arnab Bhattacharyya, Konstantin Maka...