
Speaker Vahid Liaghat Affiliation University of Maryland Host Mohit Singh Duration 01:03:07 Date recorded 8 August 2013 Consider a graph G=(V,E) with a weight value w(v) associated with each vertex v. A demand is a pair of vertices (s,t). A subgraph H satisfies the demand if s and t are connected in H. In the (offline) nodeweighted Steiner forest problem, given a set of demands the goal is to find the minimumweight subgraph H which satisfies all demands. In the online variant, the demands arrive one by one and we need to satisfy each demand immediately; without knowing the future demands. In the online variant of the problem, we give a randomized O(log^{3}(n))competitive algorithm. The competitive ratio is tight to a logarithmic factor. This result generalizes the recent result of Naor, Panigrahi, and Singh for the Steiner tree problem, thus answering one of their open problems. When restricted to planar graphs (and more generally graphs excluding a fixed minor) we give a deterministic primaldual algorithm with a logarithmic competitive ratio which is tight to a constant factor.
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