Network Design Problems with Bounded Distances via Shallow-Light Steiner Trees

Original · EN

In a directed graph G with non-correlated edge lengths and costs, the network design problem with bounded distances asks for a cost-minimal spanning subgraph subject to a length bound for all node pairs. We give a bi-criteria (2+ε,O(n⁰.⁵⁺ε))-approximation for this problem. This improves on the currently best known linear approximation bound, at the cost of violating the distance bound by a factor of at most 2+ε. In the course of proving this result, the related problem of directed shallow-light Steiner trees arises as a subproblem. In the context of directed graphs, approximations to this problem have been elusive. We present the first non-trivial result by proposing a (1+ε,O(|R|ε))-approximation, where R are the terminals. Finally, we show how to apply our results to obtain an (α+ε,O(n⁰.⁵⁺ε))-approximation for light-weight directed α-spanners. For this, no non-trivial approximation algorithm has been known before. All running times depends on n and ε and are polynomial in n for any fixed ε>0.