Abstract. This paper presents an algorithm for constructing a spanner for ad hoc networks whose nodes have variable transmission range. Almost all previous spanner constructions fo...
Given independent random points X1, . . . , Xn ∈ Rd with common probability distribution ν, and a positive distance r = r(n) > 0, we construct a random geometric graph Gn wi...
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...
The domatic number of a graph G is the maximum number of dominating sets into which the vertex set of G can be partitioned. We show that the domatic number of a random r-regular g...
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...