Precedence-Constrained arborescences

The minimum-cost arborescence problem is a well-studied in the area of graph theory, with known polynomial-time algorithms for solving it. Previous literature introduced new variations on original different objective function and/or constraints. Recently, Precedence-Constrained Minimum-Cost Arborescence was proposed, which precedence constraints are enforced pairs vertices. These prevent formation directed paths that violate relationships along tree. We show this NP-hard, and we introduce scalable mixed integer linear programming model With respect to previous models, newly proposed performs substantially better. This work also introduces variation propose several models formulating problem.