The notion of 1-planarity is among the most natural and most studied generalizations of
graph planarity. A graph is 1-planar if it has an embedding where each edge is crossed by at …

The diameter and the radius of a graph are fundamental topological parameters that have
many important practical applications in real world networks. The fastest combinatorial …

The radius and diameter are fundamental graph parameters, with several natural definitions
for directed graphs. Each definition is well-motivated in a variety of applications. All versions …

The diameter is a fundamental graph parameter and its computation is necessary in many
applications. The fastest known way to compute the diameter exactly is to solve the All-Pairs …

δ-Hyperbolic metric spaces have been defined by M. Gromov via a simple 4-point condition:
for any four points u, v, w, x, the two larger of the sums d (u, v)+ d (w, x), d (u, w)+ d (v, x), d …

We present an explicit and efficient construction of additively weighted Voronoi diagrams on
planar graphs. Let G be a planar graph with n vertices and b sites that lie on a constant …

The focus of this book is a mathematical structure modeling a physical or biological system
that can be in any of a number of 'states.'Each state is characterized by a set of binary …

We present new algorithmic results for the class of Helly graphs, that is, for the discrete
analogues of hyperconvex metric spaces. Specifically, an undirected unweighted graph is …

Many problems in computational geometry are not stated in graph-theoretic terms, but can
be solved efficiently by constructing an auxiliary graph and performing a graph-theoretic …

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