Approximating largest convex hulls for imprecise points☆

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Abstract

Assume that a set of imprecise points in the plane is given, where each point is specified by a region in which the point will lie. Such a region can be modelled as a circle, square, line segment, etc. We study the problem of maximising the area of the convex hull of such a set. We prove NP-hardness when the imprecise points are modelled as line segments, and give linear time approximation schemes for a variety of models, based on the core-set paradigm.

Keywords

Computational geometry
Data imprecision
Convex hull
Core-sets

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This research was partially supported by the Netherlands Organisation for Scientific Research (NWO) under BRICKS/FOCUS grant number 642.065.503 and through the project GOGO.

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