Approximating Fault-Tolerant Group-Steiner Problems

In this paper, we initiate the study of designing approximation algorithms for FaultTolerant Group-Steiner (FTGS) problems. The motivation is to protect the well-studied group-Steiner networks from edge or vertex failures. In Fault-Tolerant Group-Steiner problems, we are given a graph with edge(or vertex-) costs, a root vertex, and a collection of subsets of vertices called groups. The objective is to find a minimum-cost subgraph that has two edge(or vertex-) disjoint paths from each group to the root. We present approximation algorithms and hardness results for several variants of this basic problem, e.g., edge-costs vs. vertex-costs, edge-connectivity vs. vertex-connectivity, and 2-connecting from each group a single vertex vs. two distinct vertices from each group. Main contributions of our paper include the introduction of general structural lemmas on connectivity and a charging scheme that may find more applications in the future. Our algorithmic results are supplemented by inapproximability results, which are tight in some cases. ∗IBM T.J.Watson Research Center. Email: [email protected] †Rutgers University, Camden. Email: [email protected] Partially supported by NSF grant 08129959 ‡The Open University of Israel. Email: [email protected]