### Additive Approximation for Bounded Degree Survivable Network Design

Lap Chi Lau, Mohit Singh
2013 SIAM journal on computing (Print)
In the minimum bounded degree Steiner network problem, we are given an undirected graph with an edge cost for each edge, a connectivity requirement r uv for each pair of vertices u and v, and a degree upper bound b v for each vertex v. The task is to find a minimum cost subgraph that satisfies all the connectivity requirements and degree upper bounds. Let r max := max u,v {r uv } and OPT be the cost of an optimal solution that satisfies all the degree bounds. We present approximation algorithms
more » ... that minimize the total cost and the degree violation simultaneously. • In the special case when r max = 1, there is a polynomial time algorithm that returns a Steiner forest of cost at most 2OPT and the degree of each vertex v is at most b v + 3. • In the general case, there is a polynomial time algorithm that returns a Steiner network of cost at most 2OPT and the degree of each vertex v is at most b v + 6r max + 3. * A preliminary version appeared in