Three algorithmic approaches to the general position problem

Abstract

If $G$ is a graph, then $X\subseteq V(G)$ is a general position set if for every two vertices $v,u\in X$ and every shortest $(u,v)$-path $P$, it holds that no inner vertex of $P$ lies in $X$. In this note we propose three algorithms to compute a largest general position set in $G$: an integer linear programming algorithm, a genetic algorithm, and a simulated annealing algorithm. These approaches are supported by examples from different areas of graph theory.