On Optimal \(w\)-gons in Convex Polygons

Let \(P\) be a set of \(n\) points in \(\mathbb{R}^2\). For a given positive integer \(w<n\), our objective is to find a set \(C \subset P\) of points, such that \(CH(P\setminus C)\) has the smallest number of vertices and \(C\) has at most \(n-w\) points. We discuss the \(O(wn^3)\) time dynamic...

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Bibliographic Details
Published inarXiv.org
Main Author Keikha, Vahideh
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 02.03.2021
Subjects
Algorithms
Apexes
Dynamic programming
Polygons
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Summary:Let \(P\) be a set of \(n\) points in \(\mathbb{R}^2\). For a given positive integer \(w<n\), our objective is to find a set \(C \subset P\) of points, such that \(CH(P\setminus C)\) has the smallest number of vertices and \(C\) has at most \(n-w\) points. We discuss the \(O(wn^3)\) time dynamic programming algorithm for monotone decomposable functions (MDF) introduced for finding a class of optimal convex \(w\)-gons, with vertices chosen from \(P\), and improve it to \(O(n^3 \log w)\) time, which gives an improvement to the existing algorithm for MDFs if their input is a convex polygon.
ISSN:2331-8422