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Data Visualization Under Uncertainity

2022 - 2024

The topic of the proposal lies in computational geometry which is a branch of theoretical computer science. Considering the objects as points is a common modeling assumption in many fields. Let D = {d1, d2, . . . , dn} be a set of imprecise points, where each imprecise point is a finite or infinite set of possible points instead of a definite point. We say that the set P = {p1, p2, . . . , pn} realizes D if pi belongs to di for all values of i. The assumption of representing an imprecision point by a disk, for instance, is common, since the measuring devices (for instance GPS devices) usually have a predetermined value of the error of estimation. In this proposal, we study several computations on some theoretical problems in computer science and mathematics under the assumption that the input is imprecise. We mainly focus on preprocessing input regions to speed up further computations. In particular, we study some computations on the networks constructed on imprecise inputs and also basic measurements of a point set such as convex hull or separability of imprecise points (which we assume we also assigned some colors).