|DATE:||Wednesday, March 15th|
|TIME:||4:30 PM - 5:30 PM|
|TITLE:||Approximability of the Minimum-Cost k-Connected Spanning Subgraph Problem|
|SPEAKER:||Artur Czumaj, New Jersey Institute of Technology|
Further, I will briefly explain the extension of this approach to a PTAS for finding a minimum-cost k-edge connected graph/multigraph spanning a set of points in a multi-dimensional Euclidean space and to a PTAS for the problem of Euclidean minimum-cost Steiner biconnectivity.
In the second part of the talk I will discuss hardness of approximations for the minimum-cost k-vertex- and k-edge-connected spanning subgraph problems. The only inapproximability result known so far states that the k-edge-connectivity problem in unweighted graphs does not have a PTAS unless P=NP, even for k=2. I shall present a simpler proof of this result that holds even for graphs of bounded degree, and provide the first proof that finding a PTAS for the k-vertex-connectivity problem in unweighted graphs is NP-hard even for k=2 and for graphs of bounded degree.
This is a joint work Andrzej Lingas (Lund University, Sweden)