Bernd Zey

Solving Two-Stage Stochastic Steiner Tree Problems by Two-Stage Branch-and-Cut

We consider the Steiner tree problem under a 2-stage stochastic model with recourse and finitely many scenarios (SSTP). Thereby, edges are purchased in the first stage when only probabilistic information on the set of terminals and the future edge costs is known. In the second stage, one of the given scenarios is realized and additional edges are purchased to interconnect the set of (now known) terminals. The goal is to choose an edge set to be purchased in the first stage while minimizing the overall expected cost of the solution.

On the Hardness and Approximability of Planar Biconnectivity Augmentation

Given a planar graph G = (V ,E ), the planar biconnectivity augmentation problem (PBA) asks for an edge set E *** *** V ×V such that G + E *** is planar and biconnected. This problem is known to be

Stochastic Survivable Network Design Problems

\mathcal{NP}

Improved steiner tree algorithms for bounded treewidth

-hard in general; see [1]. We show that PBA is already

Parameterized Algorithms for Stochastic Steiner Tree Problems

\mathcal{NP}

Stochastic Survivable Network Design Problems: Theory and Practice

-hard if all cutvertices of G belong to a common biconnected component B *, and even remains

Improved Steiner tree algorithms for bounded treewidth

\mathcal{NP}

Planar Biconnectivity Augmentation with Fixed Embedding

-hard if the SPQR-tree of B * (excluding Q-nodes) has a diameter of at most two. For the latter case, we present a new 5/3-approximation algorithm with runtime

ILP formulations for the two-stage stochastic Steiner tree problem.

{\mathcal{O}}(|V|^{2.5})

MIP Formulations for the Steiner Forest Problem.

. Though a 5/3-approximation of PBA has already been presented [12], we give a family of counter-examples showing that this algorithm cannot achieve an approximation ratio better than 2, thus the best known approximation ratio for PBA is 2.