Random polygon generation using ‘GRP_AS’ heuristic

Abstract

Random polygon Generation from a given set of points is very important for different applications. A heuristic termed as “GRP_AS” has been proposed here to generate a random simple polygon from a given set of `n' points in 2-Dimensional plane. The “2-Opt Move” heuristic with time complexity O(n <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</sup> ) is the best known among the existing heuristics to generate a simple polygon. We recently designed another heuristic “GRP_CH” for the same problem with time complexity O(n <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> ) which was shown to be better than that of “2-Opt Move” heuristic in terms of random behaviour and time complexity. In this work, our main objective is to design an algorithm with reduced time complexity. The proposed heuristic, “GRP_AS” is based on the principle of random selection of a line segment and angular sorting of the point set. This “GRP_AS” heuristic takes O(nlogn) time which is less than that of “2-Opt Move” heuristic as well as “GRP_CH” heuristic. The lower bound and upper bound on the number of polygons generated in “GRP_AS” heuristic has been computed.