A (unit) disk graph is the intersection graph of closed (unit) disks in the plane. Almost three
decades ago, an elegant polynomial-time algorithm was found for Maximum Clique on unit …

We show for several planar and geometric problems that the best known approximation
schemes are essentially optimal with respect to the dependence on epsi. For example, we …

We initiate a systematic study of approximation schemes for fundamental optimization
problems on disk graphs, a common generalization of both planar graphs and unit-disk …

This paper studies maximum multicommodity flow and maximum concurrent flow in multihop
wireless networks subject to both bandwidth and interference constraints. The existing proof …

We present the first study on the approximability of geometric versions of the unique
coverage problem and the minimum membership set cover problem. In the former problem …

In a disk graph, every vertex corresponds to a disk in $\mathbb {R}^ 2$ and two vertices are
connected by an edge whenever the two corresponding disks intersect. Disk graphs form an …

Can a combinatorial optimization problem be approximated better if it is determined by a
system of geometric objects? Many combinatorial optimization problems are NP-hard to …

We investigate a fundamental vertex-deletion problem called (Induced) Subgraph Hitting:
given a graph $ G $ and a set $\mathcal {F} $ of forbidden graphs, the goal is to compute a …

We propose a polynomial-time algorithm which takes as input a finite set of points of R^ 3
and computes, up to arbitrary precision, a maximum subset with diameter at most 1. More …

For intersection graphs of disks and other fat objects, polynomial-time approximation
schemes are known for the independent set and vertex cover problems, but the existing …