Let P be a set of n points in the plane. In the traditional geometric algorithms view, P is given as an unordered sequence of locations (usually pairs of x and y coordinates). There are many interesting and useful structures that one can build on top of P: the Delaunay triangulation, Voronoi diagram, well-separated pair decomposition, quadtree, etc. These structures can all be represented in O(n) space but take Omega(n log n) time to construct on a Real RAM, and, hence, contain information about P that is encoded in P but cannot be directly read from P.

In this talk I will explore the question how much information about the
structure of a set of points can be derived from their locations, especially
when we are *uncertain* about the locations of the points.

In the standard model of computation often taught in computer science courses one identifies elementary operations and counts them in order to obtain the runtime. However, given the complexity of computing hardware, this measure often does not correlate well with actual observed runtime on a computer; accessing n items sequentially or randomly typically have runtimes that differ by several orders of magnitude. In this talk I will present the cache-oblivious model of computation, a model that was introduced by Prokop in 1999 and is relatively easy to reason with, by modeling the multilevel caches that are a defining feature of the cost of modern computation. After presenting the model, several data structure and algorithms that illustrate design techniques to develop cache-obliviously optimal structures will be presented.