Minimum dispersion problems

Minimum Power Connectivity Problems

Given a (directed or undirected) graph with costs on the edges, the power of a node is the maximum cost of an edge leaving it, and the power of the graph is the sum of the powers of its nodes. Motivated by applications for wireless networks, we consider some fundamental network design problems under the power minimization criteria. Let G = (V, E) be a graph with edge-costs {ce : e ∈ E} and let ...

Minimum-diameter covering problems

A set V and a collection of (possibly non-disjoint) subsets are given. Also given is a real matrix describing distances between elements of V. A cover is a subset of V containing at least one representative from each subset. The multiple-choice minimum diameter problem is to select a cover of minimum diameter. The diameter is deened as the maximum distance of any pair of elements in the cover. ...

Minimum Rank Problems

A graph describes the zero-nonzero pattern of a family of matrices, with the type of graph (undirected or directed, simple or allowing loops) determining what type of matrices (symmetric or not necessarily symmetric, diagonal entries free or constrained) are described by the graph. The minimum rank problem of the graph is to determine the minimum among the ranks of the matrices in this family; ...

Minimum loss scheduling problems

We consider two minimum loss scheduling problems. Let the arrival epochs and processing times of n consecutive jobs be known. The first problem deals with the case these jobs can be processed by m parallel nonidentical machines without waiting room, i.e., a pure loss system. In the second problem there is one machine with a finite waiting room, i.e., a single machine delay-loss system. For both...

Approximation of Geometri Dispersion Problems