Inference Maximizing Point Configurations for Parsimonious Algorithms

We present an exploration of inferring orientations for point configurations. We can compute the orientation of every triple of points by a combination of direct calculation and inference from prior computations. This ''parsimonious'' approach was suggested by Knuth in 1992, and aims to minimize calculation by maximizing inference. We wish to investigate the efficacy of this approach by investigating the minimum and maximum number of inferences that are possible for a point set configuration. To find the configurations which yield maximum inferences, there is no direct formula and hence two constructive approaches are suggested. A basic analysis of sequences that achieve those maximum inferences is also presented and some properties have been proved regarding their existence. Our problem is found to be related to the famous ''Empty Triangle'' problem, an Erdős-class problem in Discrete Geometry. Hence our work could potentially shed light on this problem.