On Optimal w-gons in Convex Polygons

03/02/2021

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by   Vahideh Keikha, et al.

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Let P be a set of n points in ℝ^2. For a given positive integer w<n, our objective is to find a set C ⊂ P of points, such that CH(P∖ 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.