@article {IOPORT.05924704, author = {Cabello, Sergio and Rote, G\"unter}, title = {Obnoxious centers in graphs.}, year = {2010}, journal = {SIAM Journal on Discrete Mathematics}, volume = {24}, number = {4}, issn = {0895-4801}, pages = {1713-1730}, publisher = {Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA}, doi = {10.1137/09077638X}, abstract = {Summary: We consider the problem of finding obnoxious centers in graphs. For arbitrary graphs with $n$ vertices and $m$ edges, we give a randomized algorithm with $O(n\log^{2}n+m\log n)$ expected time. For planar graphs, we give algorithms with $O(n\log n)$ expected time and $O(n\log^{3}n)$ worst-case time. For graphs with bounded treewidth, we give an algorithm taking $O(n\log n)$ worst-case time. The algorithms make use of parametric search and several results for computing distances on graphs of bounded treewidth and planar graphs.}, identifier = {05924704}, }