Algorithms for Single-Source Vertex Connectivity

In the Survivable Network Design Problem (SNDP) the goal is to find a minimum cost subset of edges that satisfies a given set of pairwise connectivity requirements among the vertices. This general network design framework has been studied extensively and is tied to the development of major algorithmic techniques. For the edge-connectivity version of the problem, a 2-approximation algorithm is known for arbitrary pairwise connectivity requirements. However, no non-trivial algorithms are known for its vertex connectivity counterpart. In fact, even highly restricted special cases of the vertex connectivity version remain poorly understood. We study the single-source k-vertex connectivity version of SNDP. We are given a graph G(V, E) with a subset T of terminals and a source vertex s, and the goal is to find a minimum cost subset of edges ensuring that every terminal is k-vertex connected to s. Our main result is an O(k log n)-approximation algorithm for this problem; this improves upo...

• Type: Conference
• Year: 2008
• Where: FOCS
• Authors: Julia Chuzhoy, Sanjeev Khanna
• Keywords: FOCS 2008, Minimum Cost Subset, Pairwise Connectivity Requirements, Theoretical Computer Science, Vertex Connectivity