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...Advanced geometric algorithms lecture notes vladlen koltun spring computer science department serra mall gates stanford university ca usa edu contents preliminaries from convex geometry denitions radon s theorem helly carath eodory nets and vc dimension dening the existence of small samples bounding applications arrangements point location segment intersection searching range nearest neighbor search centerpoints planar graphs separators rado centerpoint drawing in plane euler formula coloring koebe well separated pair decompositions their wspddenition closest all neighbors spanners euclidean minimum spanning trees diameter constructing wspds i introducing quadtrees compressed traveling salesperson background algorithm approximating extent sets width coresets ii...