Robust capacitated Steiner trees and networks with uniform demands

Robust capacitated trees and networks with uniform demands

We are interested in the design of robust (or resilient) capacitated rooted Steiner networks in case of terminals with uniform demands. Formally, we are given a graph, capacity and cost functions on the edges, a root, a subset of nodes called terminals, and a bound k on the number of edge failures. We first study the problem where k = 1 and the network that we want to design must be a tree cove...

Robust Reoptimization of Steiner Trees

In reoptimization problems, one is given an optimal solution to a problem instance and a local modification of the instance. The goal is to obtain a solution for the modified instance. The additional information about the instance provided by the given solution plays a central role: we aim to use that information in order to obtain better solutions than we are able to compute from scratch. In t...

Rotationally optimal spanning and Steiner trees in uniform orientation metrics

We consider the problem of finding a minimum spanning and Steiner tree for a set of points in the plane where the orientations of edge segments are restricted to uniformly distributed orientations, , and where the coordinate system can be rotated around the origin by an arbitrary angle. The most important cases with applications in VLSI design arise when or . In the former, so-called rectilinea...

Practical Approximations of Steiner Trees in Uniform Orientation Metrics

The Steiner minimum tree problem, which asks for a minimum-length interconnection of a given set of terminals in the plane, is one of the fundamental problems in Very Large Scale Integration (VLSI) physical design. Although advances in VLSI manufacturing technologies have introduced additional routing objectives, minimum length continues to be the primary objective when routing non-critical net...

Steiner Trees and Steiner Forests