Handouts:
4/1/09: More on Voronoi diagrams and Delaunay diagrams

More on Voronoi diagrams and their applications. I present powerpoint slides.
Discussion of geometric TSP: it is "NP-hard" to solve optimally. 2-approximation (double MST and shortcut to get a tour), 1.5-approximation of Christofides, and 1+epsilon approximation of Arora/Mitchell (a "PTAS": Polynomial-Time Approximation Scheme).
Bottom line: For any FIXED epsilon and FIXED dimension d, one can find an approximately optimal TSP tour, within a factor 1+epsilon of optimal, on a set of n points in d dimensions in time O(n log n). WARNING: The "big Oh" hides an enormous constant that depends on epsilon and d.