Obnoxious centers in graphs

We consider the problem of finding obnoxious centers in graphs. For arbitrary graphs with <i>n</i> vertices and <i>m</i> edges, we give a randomized algorithm with <i>O</i>(<i>n</i> log<sup>2</sup> <i>n</i> + <i>m</i> log <i>n</i>) expected time. For planar graphs, we give algorithms with <i>O</i>(<i>n</i> log <i>n</i>) expected time and <i>O</i>(<i>n</i> log<sup>3</sup> <i>n</i>) worst-case time. For graphs with bounded treewidth, we give an algorithm taking <i>O</i>(<i>n</i> log <i>n</i>) worst-case time. The algorithms make use of parametric search and several results for computing distances on graphs of bounded treewidth and planar graphs.

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