Beyond Tree Embeddings – a Deterministic Framework for Network Design with Deadlines or Delay
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We consider network design problems with deadline or delay. All previous results for these models are based on randomized embedding of the graph into a tree (HST) and then solving the problem on this tree. We show that this is not necessary. In particular, we design a deterministic framework for these problems which is not based on embedding. This enables us to provide deterministic poly-log(n)-competitive algorithms for Steiner tree, generalized Steiner tree, node weighted Steiner tree, (non-uniform) facility location and directed Steiner tree with deadlines or with delay (where n is the number of nodes). Our deterministic algorithms also give improved guarantees over some previous randomized results. In addition, we show a lower bound of poly-log(n) for some of these problems, which implies that our framework is optimal up to the power of the poly-log. Our algorithms and techniques differ significantly from those in all previous considerations of these problems.
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