GA for straight-line grid drawings of maximal planar graphs

Abstract

A straight-line grid drawing of a planar graph G of n vertices is a drawing of G on an integer grid such that each vertex is drawn as a grid point and each edge is drawn as a straight-line segment without edge crossings. Finding algorithms for straight-line grid drawings of maximal planar graphs (MPGs) in the minimum area is still an elusive goal. In this paper we explore the potential use of genetic algorithms to this problem and various implementation aspects related to it. Here we introduce a genetic algorithm, which nicely draws MPG of moderate size. This new algorithm draws these graphs in a rectangular grid with area ⌊2(n-1)/3⌋×⌊2(n-1)/3⌋ at least, and that this is optimal area (proved mathematically). Also, the novel issue in the proposed method is the fitness evaluation method, which is less costly than a standard fitness evaluation procedure. It is described, tested on several MPG.