Approximating Subset k-Connectivity Problems
نویسنده
چکیده
A subset T ⊆ V of terminals is k-connected to a root s in a directed/undirected graph J if J has k internally-disjoint vs-paths for every v ∈ T ; T is k-connected in J if T is k-connected to every s ∈ T . We consider the Subset k-Connectivity Augmentation problem: given a graph G = (V,E) with edge/node-costs, node subset T ⊆ V , and a subgraph J = (V,EJ ) of G such that T is k-connected in J , find a minimum-cost augmenting edge-set F ⊆ E \ EJ such that T is (k + 1)-connected in J ∪ F . The problem admits trivial ratio O(|T |). We consider the case |T | > k and prove that for directed/undirected graphs and edge/node-costs, a ρ-approximation for Rooted Subset k-Connectivity Augmentation implies the following ratios for Subset k-Connectivity Augmentation:
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