Abstract
In this paper, we initiate the study of designing approximation algorithms for Fault-Tolerant 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 a single vertex vs. two distinct vertices from each group. The 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.
| Original language | English |
|---|---|
| Pages (from-to) | 55-64 |
| Number of pages | 10 |
| Journal | Theoretical Computer Science |
| Volume | 416 |
| DOIs | |
| State | Published - 27 Jan 2012 |
Bibliographical note
Funding Information:We would like to thank an anonymous referee for his comments that helped considerably improve the presentation of the paper. The second author was partially supported by NSF grant 08129959.
Keywords
- Approximation algorithms
- Connectivity
- Fault tolerance
- Group Steiner