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| | == Speaker == | | == Speaker == |
| | Vahid Liaghat, University of Maryland | | Vahid Liaghat, University of Maryland |
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| − | == Abstract ==
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| − | 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) node-weighted Steiner forest problem, given a set of demands the goal is to find the minimum-weight 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.
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| − | 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 et al. which is an O(log^3(n))-competitive algorithm 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 primal-dual algorithm with a logarithmic competitive ratio which is tight to a constant factor.
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