Largest area convex hull of axis-aligned squares based on imprecise data

Abstract

Data collected from real world are often imprecise. A few algorithms were proposed recently to compute the convex hull of maximum area when the axis-aligned squares model is used to represent imprecise input data. If squares are non-overlapping and of different sizes, the time complexity of the best known algorithm is O(n7). If squares are allowed to overlap but have the same size, the time complexity of the best known algorithm is O(n 5). In this paper, we improve both bounds by a quadratic factor, i.e., to O(n5) and O(n3), respectively. © 2011 Springer-Verlag.