In this paper the authors study the following problem, which they call the weighted routing problem. Let be given a graph G=(V,E) with non-negative edge weights we∈RÅ+ and let N=∈T1,...,Tn∈, N∈1, be a list of node sets. The weighted routing problem consists in finding mutually disjoint edge sets S1,...,SN such that, for each k∈∈1,...,N∈, the subgraph (V(Sk),Sk) contains an [s,t]-path for all s,t∈Tk and the sum of the weights of the edge sets is minimal. The present motivation for studying this problem arises from the routing problem in VLSI-design, where given sets of points have to be connected by wires. The authors consider the weighted routing problem from a polyhedral point of view. They define an appropriate polyhedron and try to (partially) describe this polyhedron by means of inequalities. The authors describe our separation algorithms for some of the presented classes of inequalities. Based on these separation routines they have implemented a branch and cut algorithm. Our algorithm is applicable to an important subclass of routing problems arising in VLSI-design, namely to switchbox routing problems where the underlying graph and the list of node sets is located on the outer face of the grid. The authors report on the present computational experience with this class of problem instances.
