Approximating Maximum Diameter-Bounded Subgraph in Unit Disk Graphs

The Maximum Degree-and-Diameter-Bounded Subgraph in the Mesh

The problem of finding the largest connected subgraph of a given undirected host graph, subject to constraints on the maximum degree ∆ and the diameter D, was introduced in [1], as a generalization of the Degree-Diameter Problem. A case of special interest is when the host graph is a common parallel architecture. Here we discuss the case when the host graph is a k-dimensional mesh. We provide s...

The Maximum Degree & Diameter-Bounded Subgraph and its Applications

We introduce the problem of finding the largest subgraph of a given weighted undirected graph (host graph), subject to constraints on the maximum degree and the diameter. We discuss some applications in security, network design and parallel processing, and in connection with the latter we derive some bounds for the order of the largest subgraph in host graphs of practical interest: the mesh and...

On approximating the maximum diameter ratio of graphs

It is proved that computing the maximum diameter ratio also known as the local density of a graph is APX complete The related problem of nding a maximum subgraph of a xed diameter d is proved to be even harder to approximate

The Maximum Indpendent Set Problem in Unit Disk Graphs

The class of intersection graphs of disks in the Euclidean plane, called disk graphs, was studied for many years for its theoretical aspects as well as for its applications. The maximum independent set problem on disk graphs (computing a largest subset of the given disks such that the disks in the subset are pairwise disjoint) has applications in map labeling. Under the assumption that labels o...

Approximation Algorithms for Maximum Cliques in 3D Unit-Disk Graphs