Reduction of Two-Dimensional Data for Speeding Up Convex Hull Computation

TL;DR

This paper introduces an efficient incremental algorithm for computing 2D convex hulls by reducing data points through a novel extremal point classification method, significantly improving computation speed.

Contribution

It presents a new data reduction technique that applies Graham's scan only on a subset of extremal points, enhancing convex hull computation efficiency.

Findings

Algorithm operates in linear time relative to data points.

Data reduction method decreases the number of points for convex hull calculation.

Method is effective for large 2D datasets.

Abstract

An incremental approach for computation of convex hull for data points in two-dimensions is presented. The algorithm is not output-sensitive and costs a time that is linear in the size of data points at input. Graham's scan is applied only on a subset of the data points, represented at the extremal of the dataset. Points are classified for extremal, in proportion with the modular distance, about an imaginary point interior to the region bounded by convex hull of the dataset assumed for origin or center in polar coordinate. A subset of the data is arrived by terminating at until an event of no change in maximal points is observed per bin, for iteratively and exponentially decreasing intervals.