Online Node-weighted Steiner Forest and Extensions

Опубликовано 27 июля 2016, 2:00

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. 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 primal-dual algorithm with a logarithmic competitive ratio which is tight to a constant factor.