Improved approximation algorithms for degree-bounded network design problems with node connectivity requirements

We consider degree bounded network design problems with element and vertex connectivity requirements. In the degree bounded Survivable Network Design (SNDP) problem, the input is an undirected graph G = (V, E) with weights w(e) on the edges and degree bounds b(v) on the vertices, and connectivity requirements r(uv) for each pair uv of vertices. The goal is to select a minimum-weight subgraph H of G that meets the connectivity requirements and it satisfies the degree bounds on the vertices: for each pair uv of vertices, H has r(uv) disjoint paths between u and v; additionally, each vertex v is incident to at most b(v) edges in H. We give the first (O(1), O(1) · b(v)) bicriteria approximation algorithms for the degree-bounded SNDP problem with element connectivity requirements and for several degree-bounded SNDP problems with vertex connectivity requirements. Our algorithms construct a subgraph H whose weight is at most O(1) times the optimal such that each vertex v is incident to at most O(1) · b(v) edges in H. We can also extend our approach to network design problems in directed graphs with out-degree constraints to obtain (O(1), O(1) · b+(v)) bicriteria approximation.