Network design with weighted degree constraints

In an undirected graph G=(V,E)G=(V,E) with a weight function w:E×V→Q+w:E×V→Q+, the weighted degree dw(v;E)dw(v;E) of a vertex vv is defined as ∑{w(e,v)∣e∈Eincident tov}. In this paper, we consider a network design problem which has upper-bounds on weighted degrees of vertices as its constraints while the objective is to compute a minimum cost graph with a prescribed connectivity. We propose bi-criteria approximation algorithms based on iterative rounding, which has been successfully applied to the degree-bounded network design problem. A problem of minimizing the maximum weighted degree of vertices is also discussed.