A Simple Convex Layers Algorithm
Raimi A. Rufai, Dana S. Richards

TL;DR
This paper introduces a new, simple, and optimal algorithm for computing convex layers in a set of points, achieving the best theoretical runtime with practical simplicity.
Contribution
The paper presents a novel algorithm that computes convex layers efficiently using monotone convex chains, simplifying implementation while maintaining optimal runtime.
Findings
Achieves $ ext{O}(n ext{log} n)$ runtime and linear space complexity.
Uses four sets of monotone convex chains for computation.
Merges chains efficiently to compute convex layers.
Abstract
Given a set of points in the plane, the first layer of is formed by the points that appear on 's convex hull. In general, a point belongs to layer , if it lies on the convex hull of the set . The \emph{convex layers problem} is to compute the convex layers . Existing algorithms for this problem either do not achieve the optimal runtime and linear space, or are overly complex and difficult to apply in practice. We propose a new algorithm that is both optimal and simple. The simplicity is achieved by independently computing four sets of monotone convex chains in time and linear space. These are then merged in time.
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Taxonomy
TopicsComputational Geometry and Mesh Generation · Digital Image Processing Techniques · Advanced Graph Theory Research
