Tree Embeddings for Two-Edge-Connected Network Design

The group Steiner problem is a classical network design problem where we are given a graph and a collection of groups of vertices, and want to build a min-cost subgraph that connects the root vertex to at least one vertex from each group. What if we wanted to build a subgraph that two-edge-connects the root to each group--that is, for every group g V , the subgraph should contain two edge-disjoint paths from the root to some vertex in g? What if we wanted the two edgedisjoint paths to end up at distinct vertices in the group, so that the loss of a single member of the group would not destroy connectivity? In this paper, we investigate tree-embedding techniques that can be used to solve these and other 2-edgeconnected network design problems. We illustrate the potential of these techniques by giving poly-logarithmic approximation algorithms for two-edge-connected versions of the group Steiner, connected facility location, buy-at-bulk, and the k-MST problems.

• Type: Conference
• Year: 2010
• Where: SODA
• Authors: Anupam Gupta, Ravishankar Krishnaswamy, R. Ravi
• Keywords: Discrete Algorithms, Group Steiner Problem, Min-cost Subgraph, Root Vertex, SODA 2010